number - an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.

$100 fee plus $30 per month. Write an expression that describes the cost of a gym membership after m

$100 fee plus $30 per month. Write an expression that describes the cost of a gym membership after m months.
Set up the cost function C(m) where m is the number of months you rent:
C(m) = Monthly membership fee * m + initial fee
[B]C(m) = 30m + 100[/B]

$3.75 in quarters and nickles in her car. The number of nickles is fifteen more than the number of q

$3.75 in quarters and nickels in her car. The number of nickels is fifteen more than the number of quarters. How many of each type of coin does she have?
Let the number of nickels be n, and the number of quarters be q. We know nickels are 0.05, and quarters are 0.25. We're given:
[LIST=1]
[*]n = q + 15
[*]0.05n + 0.25q = 3.75
[/LIST]
Substituting (1) into (2), we get:
0.05(q + 15) + 0.25q = 3.75
0.05q + 0.75 + 0.25q = 3.75
Combine like term:
0.3q + 0.75 = 3.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.3q%2B0.75%3D3.75&pl=Solve']Typing this equation into our calculator[/URL], we get:
[B]q = 10[/B]
Substituting q = 10 into Equation (1), we get:
n = 10 + 15
[B]n = 25[/B]

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, w

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, written as a decimal (1%=.01, 2%=.02,etc) , n=number of times per year, t= number of years
So we have:
[LIST]
[*]$300 principal
[*]13 * 2 = 26 periods for n
[*]Rate r for a semiannual compound is 8%/2 = 4% per 6 month period
[/LIST]
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=300&int=4&t=26&pl=Compound+Interest']compound interest with balance calculator[/URL], we get:
[B]$831.74[/B]

$45 and you add $2.25 each day

$45 and you add $2.25 each day
Let d be the number of days. Our Cost function C(d) is:
[B]C(d) = 2.25d + 45[/B]

$6500 is 7/10 of a number. What is the number

The number is $9,285 from our [URL='http://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=6500&pct1=70&pcheck=2&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pof1=40&pof2=20&pl=Calculate']percentage-decimal-fraction calculator[/URL].

π Digits

Calculates PI (π) to a set number of decimal places using the Gauss-Legendre Algorithm.

-11, -9, -7, -5, -3 What is the next number? What is the 200th term in this sequence?

-11, -9, -7, -5, -3 What is the next number? What is the 200th term in this sequence?
We see that Term 1 is -11, Term 2 is -9, so we do a point slope equation of (1,-11)(2,-9) to get the [URL='https://www.mathcelebrity.com/search.php?q=%281%2C-11%29%282%2C-9%29']nth term of the formula[/URL]
f(n) = 2n - 13
The next number is the 6th term:
f(6) = 2(6) - 13
f(6) = 12 - 13
f(6) = [B]-1
[/B]
The 200th term is:
f(200) = 2(200) - 13
f(200) = 400 - 13
f(200) = [B]387[/B]

-28 is the solution to the sum of a number p and 21

-28 is the solution to the sum of a number p and 21
The sum of a number p and 21:
p + 21
The phrase [I]is the solution to[/I] means an equation, so we set p + 21 equal to -28:
[B]p + 21 = -28
[/B]
If the problem asks you to solve for p, then we [URL='https://www.mathcelebrity.com/1unk.php?num=p%2B21%3D-28&pl=Solve']type this into our search engine[/URL] and we get:
p = [B]-49[/B]

-65 times the difference between a number and 79 is equal to the number plus 98

-65 times the difference between a number and 79 is equal to the number plus 98
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The first expression, [I]the difference between a number and 79[/I] means we subtract 79 from our arbitrary variable of x:
x - 79
Next, -65 times the difference between a number and 79 means we multiply our result above by -65:
-65(x - 79)
The phrase [I]the number[/I] refers to the arbitrary variable x earlier. The number plus 98 means we add 98 to x:
x + 98
Now, let's bring it all together. The phrase [I]is equal to[/I] means an equation. So we set -65(x - 79) equal to x + [B]98:
-65(x - 79) = x + 98[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=-65%28x-79%29%3Dx%2B98&pl=Solve']type this equation into our search engine[/URL], and you get:
x = [B]76.31818[/B]

-n = n

-n = n
Add n to each side:
-n + n = n + n
Cancel the n's on the left side:
0 = 2n
Only number that solves this is [B]n = 0[/B]

0,7,14,21 What is the next number? What is the 1000th term?

0,7,14,21
What is the next number?
What is the 1000th term?
We're adding 7 to the last term, so we get a next term of:
21 + 7 = [B]28
[/B]
For our nth term, we notice a pattern for the nth term of:
7n - 7
[LIST]
[*]n = 1 --> 7(1) - 7 = 0
[*]n = 2 --> 7(2) - 7 = 7
[*]n = 3 --> 7(3) - 7 = 14
[/LIST]
For n = 1000, we have:
7(1000) - 7 = 7000 - 7 = [B]6993[/B]

1 box is used every 1.5 days. How many are used in 242 days?

1 box is used every 1.5 days. How many are used in 242 days?
Set up a proportion of boxes to days where b is the number of boxes used for 242 days:
1/1.5 = b/242
To solve this proportion for b, we [URL='https://www.mathcelebrity.com/prop.php?num1=1&num2=b&den1=1.5&den2=242&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
b = [B]161.3333[/B]

1 Die Roll

Calculates the probability for the following events in the roll of one fair dice (1 dice roll calculator or 1 die roll calculator):

* Probability of any total from (1-6)

* Probability of the total being less than, less than or equal to, greater than, or greater than or equal to (1-6)

* The total being even

* The total being odd

* The total being a prime number

* The total being a non-prime number

* Rolling a list of numbers i.e. (2,5,6)

* Simulate (n) Monte Carlo die simulations.

1 die calculator

* Probability of any total from (1-6)

* Probability of the total being less than, less than or equal to, greater than, or greater than or equal to (1-6)

* The total being even

* The total being odd

* The total being a prime number

* The total being a non-prime number

* Rolling a list of numbers i.e. (2,5,6)

* Simulate (n) Monte Carlo die simulations.

1 die calculator

1, 1/2, 1/3, 1/4, 1/5 What is the next number? What is the 89th term of the sequence?

1, 1/2, 1/3, 1/4, 1/5
What is the next number?
What is the 89th term of the sequence?
Formula for nth term is 1/n
Next number is n = 5, so we have [B]1/5[/B]
With n = 89, we have [B]1/89[/B]

1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you wou

1, 1/2, 1/4, 1/8, 1/16
The next number in the sequence is 1/32. What is the function machine you would use to find the nth term of this sequence?
Hint: look at the denominators
We notice that
1/2^0 = 1/1 = 1
1/2^1 = 1/2
1/2^2 = 1/4
1/2^3 = 1/8
1/2^4 = 1/32
So we write our explicit formula for term n:
f(n) = [B]1/2^(n - 1)[/B]

1, 4, 9, 16, 25 What is the next number? What is the 50th term?

1, 4, 9, 16, 25
What is the next number?
What is the 50th term?
We see that 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25
We build a formula for the nth term:
f(n) = n^2
The next number means n = 6th term:
f(6) = 6^2 = [B]36
[/B]
The 50th term means n = 50:
f(50) = 50^2 = [B]2500[/B]

1, 9, 25, 49, .......... What is next

1, 9, 25, 49, .......... What is next
1^2 = 1
3^2 = 9
5^2 = 25
7^2 = 49
So this pattern takes odd numbers and squares them. Our next odd number is 9:
9^2 = [B]81[/B]

1/2 of a number decreased by twice a number

1/2 of a number decreased by twice a number
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]1/2 of a number: x/2
[*]Twice a number means we multiply x by 2: 2x
[*]The phrase [I]decreased by[/I] means we subtract
[/LIST]
[B]x/2 - 2x[/B]

1/2, 3, 5&1/2, 8......203 What term is the number 203?

1/2, 3, 5&1/2, 8......203
What term is the number 203?
We see the following pattern:
1/2 = 2.5*1 - 2
3 = 2.5*2 - 2
5&1/2 = 2.5*3 - 2
8 = 2.5*4 - 2
We build our function
f(n) = 2.5n - 2
Set 2.5n - 2 = 203
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2.5n-2%3D203&pl=Solve']equation solver[/URL], we get:
n = [B]82[/B]

1/3 a number increased by 10 times by that same number

1/3 a number increased by 10 times by that same number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
1/3 a number
1/3 * x = x/3
That same number means the same arbitrary variable as above:
x
10 times that same number:
10x
The phrase [I]increased by[/I] means we add:
[B]x/3 + 10x
[MEDIA=youtube]29TGt3i28jw[/MEDIA][/B]

1/3 of students at a school are boys. If there are 600 students at the school, how many are girls?

1/3 of students at a school are boys. If there are 600 students at the school, how many are girls?
If 1/3 are boys, then the number of boys is:
600 * 1/3
600/3
We [URL='https://www.mathcelebrity.com/fraction.php?frac1=600%2F3&frac2=3%2F8&pl=Simplify']type this fraction into our search engine to simplify[/URL], and we get:
200
Now we need to find how many girls are at the school:
Girls = Total Students - Boys
Girls = 600 - 200
Girls = [B]400[/B]

1/3 of the sum of a number and 2 plus 5 is -20

1/3 of the sum of a number and 2 plus 5 is -20
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
the sum of a number and 2:
x + 2
1/3 of the sum of a number and 2
1/3(x + 2)
1/3 of the sum of a number and 2 plus 5
1/3(x + 2) + 5
The phrase [I]is[/I] means equal to, so we set 1/3(x + 2) + 5 equal to -20:
[B]1/3(x + 2) + 5 = -20[/B]

1/4 of the difference of 6 and a number is 200

1/4 of the difference of 6 and a number is 200
Take this [B]algebraic expression[/B] in 4 parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The difference of 6 and a number means we subtract x from 6: 6 - x
[*]1/4 of the difference means we divide 6 - x by 4: (6 - x)/4
[*]Finally, the phrase [I]is[/I] means an equation, so we set (6 - x)/4 equal to 200
[/LIST]
[B](6 - x)/4 = 200[/B]

1/5 of the sum of the number u and 2

1/5 of the sum of the number u and 2
The sum of the number u and 2 means we add 2 to u:
u + 2
1/5 of the sum:
[B](u + 2)/5[/B]

10 more than a number z, divided by k

10 more than a number z, divided by k
The phrase [I]a number[/I] means an arbitrary variable, lets call it x.
10 more than a number means we add 10 to x:
x + 10
We divide this quantity by k:
[B](x + 10)/k[/B]

10 times a number is 420

10 times a number is 420
A number denotes an arbitrary variable, let's call it x.
10 times a number:
10x
The phrase is means equal to, so we set 10x equal to 420
[B]10x = 420 <-- This is our algebraic expression
[/B]
If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=10x%3D420&pl=Solve']equation calculator[/URL]
We get x = 42

10 times the square of a number w divided by 12

10 times the square of a number w divided by 12
The square of a number w
w^2
10 times this
10w^2
Divided by 12
[B]10w^2/12[/B]

100, 75, 50, 25, 0, -25 What is the next number? What is the 100th term?

100, 75, 50, 25, 0, -25 What is the next number? What is the 100th term?
Using point slope, we get (1, 100)(2, 75)
Our [URL='https://www.mathcelebrity.com/search.php?q=%281%2C+100%29%282%2C+75%29&x=0&y=0']series function becomes[/URL]
f(n) = -25n + 125
The next term is the 7th term:
f(7) = -25(7) + 125
f(7) = -175 + 125
f(7) = [B]-50
[/B]
The 100th term is found by n = 100:
f(100) = -25(100) + 125
f(100) = -2500 + 125
f(100) = [B]-2375[/B]

1089 Number Trick

Demonstrates the 1089 number trick for a 3 digit number that you enter

11 to the power of 6 multiply 11 to the power of 3

11 to the power of 6 multiply 11 to the power of 3
Take this in parts.
[U]Step 1: 11 to the power of 6 means we raise 11 to the 6th power using exponents:[/U]
11^6
[U]Step 2: 11 to the power of 3 means we raise 11 to the 3rd power using exponents:[/U]
11^3
[U]Step 3: Multiply each term together:[/U]
11^6 * 11^3
[U]Step 4: Simplify[/U]
Because we have 2 numbers that are the same, in this case, 11, we can add the exponents together when multiplying:
11^(6 + 3)
[B]11^9
[MEDIA=youtube]gCxVq7LqyHk[/MEDIA][/B]

12 is multiplied by some number, that product is reduced by 9, and the total is equal to 37

12 is multiplied by some number, that product is reduced by 9, and the total is equal to 37
The phrase [I]some number[/I] means an arbitrary variable, let's call it x.
12 multiplied by this number:
12x
The product of 12x is reduced by 9
12x - 9
The phrase [I]the total is equal to[/I] means an equation, so we set 12x - 9 equal to 37:
[B]12x - 9 = 37[/B]

12 plus 6 times a number is 9 times the number

12 plus 6 times a number is 9 times the number
The phrase [I]a number [/I]means an arbitrary variable. Let's call it x.
6 times a number is written as:
6x
12 plus 6 times the number means we add 6x to 12:
12 + 6x
9 times a number is written as:
9x
The phrase [I]is[/I] means an equation, so we set 12 + 6x equal to 9x
[B]12 + 6x = 9x <-- This is our algebraic expression[/B]
[B][/B]
If the problem asks you to solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B6x%3D9x&pl=Solve']type this expression into our search engine[/URL] and you get:
x = [B]4[/B]

12 plus the product of 4 and a number is greater than 72

A number means an arbitrary variable, let's call it x.
The product of 4 and a number is 4x.
12 plus that product is 4x + 12
Is greater than means an inequality, so we set the entire expression greater than 72
4x + 12 > 72

12 students want pancakes and 14 students want waffles. What is the ratio of the number of students

12 students want pancakes and 14 students want waffles. What is the ratio of the number of students who want pancakes to the total number of students?
12/14 is the initial ratio. However, we can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=12%2F14&frac2=3%2F8&pl=Simplify']So we type 12/14 into our search engine and choose simplify.[/URL] We get:
6/7

13 minutes to answer 4 problems. how many minutes would it take to answer 22 questions

13 minutes to answer 4 problems. how many minutes would it take to answer 22 questions?
Set up a proportion of time to problems where m is the number of minutes it would take for 22 questions:
13/4 = m/22
[URL='https://www.mathcelebrity.com/prop.php?num1=13&num2=m&den1=4&den2=22&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get:
m = [B]71.5[/B]

149 cars are waiting to take a ferry across the channel each ferry can only hold 18 cars how many tr

149 cars are waiting to take a ferry across the channel each ferry can only hold 18 cars how many trips will it take to get all the cars across
Number of trips = Total Cars / Cars Per ferry trip
Number of trips = 149/18
Number of trips = 8.28 trips
We round up to the next integer and we have [B]9 trips[/B]

15 added to a number is 16 times the number

15 added to a number is 16 times the number
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]15 added to a number: 15 + x
[*]16 times the number: 16x
[*]The phrase [I]is[/I] means equal to. So we set 15 + x equal to 16x
[/LIST]
[B]15 + x = 16x[/B]

15 added to the quotient of 8 and a number is 7.

15 added to the quotient of 8 and a number is 7.
Take this algebraic expression in pieces:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[*]The quotient of 8 and a number: 8/x
[*]15 added to this quotient: 8/x + 15
[*]The word [I]is[/I] means an equation, so we set 8/x + 15 equal to 7
[/LIST]
[B]8/x + 15 = 7[/B]

15 less than a number squared

15 less than a number squared
A number is denoted by an arbitrary variable, let's call it x.
x
Squared means we raise that number to a power of 2
x^2
15 less means we subtract
[B]x^2 -15[/B]

16 decreased by 3 times the sum of 3 and a number

16 decreased by 3 times the sum of 3 and a number
Take this algebraic expression in parts:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[*]The sum of 3 and a number: 3 + x
[*]3 times the sum: 3(3 + x)
[*]16 decreased by... means we subtract 3(3 + x) from 16
[/LIST]
[B]3(3 + x) from 16[/B]

180 students 1/6 are Hispanic, how many are Hispanic?

180 students 1/6 are Hispanic, how many are Hispanic?
Number of Hispanics = 180 * 1/6 = [B]30[/B]

2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than

2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than twice a number of home runs the second player hit. how many home runs did each player hit?
Declare variables:
Let the first players home runs be a
Let the second players home runs be b
We're given two equations:
[LIST=1]
[*]a = 2b + 3
[*]a + b = 60
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for a:
2b + 3 + b = 60
Using our math engine, we [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B3%2Bb%3D60&pl=Solve']type this equation[/URL] in and get:
b = [B]19
[/B]
To solve for a, we substitute b = 19 into equation (1):
a = 2(19) + 3
a = 38 + 3
a = [B]41[/B]

2 cards have different expressions written on them.: 5y - 2 and 3y + 10. for what value of y do the

2 cards have different expressions written on them.: 5y - 2 and 3y + 10. for what value of y do the 2 cards represent the same number?
If they have the same number, we set them equal to each other and solve for y:
5y - 2 = 3y + 10
To solve for y, we [URL='http://5y - 2 = 3y + 10']type this expression in our search engine [/URL]and we get:
y = [B]6[/B]

2 dice roll

Calculates the probability for the following events in a pair of fair dice rolls:

* Probability of any sum from (2-12)

* Probability of the sum being less than, less than or equal to, greater than, or greater than or equal to (2-12)

* The sum being even

* The sum being odd

* The sum being a prime number

* The sum being a non-prime number

* Rolling a list of numbers i.e. (2,5,6,12)

* Simulate (n) Monte Carlo two die simulations. 2 dice calculator

* Probability of any sum from (2-12)

* Probability of the sum being less than, less than or equal to, greater than, or greater than or equal to (2-12)

* The sum being even

* The sum being odd

* The sum being a prime number

* The sum being a non-prime number

* Rolling a list of numbers i.e. (2,5,6,12)

* Simulate (n) Monte Carlo two die simulations. 2 dice calculator

2 less than half a number

A number means we pick an arbitrary variable, let's call it "x".
Half a number is 1/2x.
2 less than that is [B]1/2x - 2[/B]

2 minus 7 times a number

A number is represented by an arbitrary variable, let's call it x.
7 times x means we multiply 7 times x.
7x
2 minus 7x is written:
2 - 7x

2 more than twice the sum of 10 and a number

2 more than twice the sum of 10 and a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of 10 and a number means we add x to 10:
10 + x
Twice the sum means we multiply 10 + x by 2:
2(10 + x)
2 more than twice the sum means we add 2 to 2(10 + x):
[B]2(10 + x) + 2[/B]

2 number Word Problems

This calculator handles word problems in the format below:

* Two numbers have a sum of 70 and a product of 1189 What are the numbers?

* Two numbers have a sum of 70. Their difference 32

* Two numbers have a sum of 70 and a product of 1189 What are the numbers?

* Two numbers have a sum of 70. Their difference 32

2 numbers add to 200. The first is 20 less than the second.

2 numbers add to 200. The first is 20 less than the second.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x + y = 200
[*]x = y - 20
[/LIST]
Plug (2) into (1)
(y - 20) + y = 200
Group like terms:
2y - 20 = 200
[URL='https://www.mathcelebrity.com/1unk.php?num=2y-20%3D200&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 110[/B] <-- This is the larger number
Plug y = 110 into Equation (2) to get the smaller number:
x = 110 - 20
[B]x = 90[/B] <-- This is the smaller number
Let's check our work for Equation (1) using x = 90, and y = 110
90 + 110 ? 200
200 = 200 <-- Good, our solutions check out for equation (1)
Let's check our work for Equation (2) using x = 90, and y = 110
90 = 110 - 20
90 = 90 <-- Good, our solutions check out for equation (2)

2 numbers that add up makes 5 but multiplied makes -36

2 numbers that add up makes 5 but multiplied makes -36
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*]x + y = 5
[*]xy = -36
[/LIST]
Rearrange equation (1) by subtracting y from each side:
[LIST=1]
[*]x = 5 - y
[*]xy = -36
[/LIST]
Substitute equation (1) for x into equation (2):
(5 - y)y = -36
5y - y^2 = -36
Add 36 to each side:
-y^2 + 5y + 36 = 0
We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=-y%5E2%2B5y%2B36%3D0&pl=Solve+Quadratic+Equation&hintnum=0']type it in our search engine and solve[/URL] to get:
y = ([B]-4, 9[/B])
We check our work for each equation:
[LIST=1]
[*]-4 + 9 = -5
[*]-4(9) = -36
[/LIST]
They both check out

2 numbers that are equal have a sum of 60

2 numbers that are equal have a sum of 60
Let's choose 2 arbitrary variables for the 2 numbers
x, y
Were given 2 equations:
[LIST=1]
[*]x = y <-- Because we have the phrase [I]that are equal[/I]
[*]x + y = 60
[/LIST]
Because x = y in equation (1), we can substitute equation (1) into equation (2) for x:
y + y = 60
Add like terms to get:
2y = 60
Divide each side by 2:
2y/2 = 60/2
Cancel the 2's and we get:
y = [B]30
[/B]
Since x = y, x = y = 30
x = [B]30[/B]

2 times a number added to another number is 25. 3 times the first number minus the other number is 2

2 times a number added to another number is 25. 3 times the first number minus the other number is 20.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]2x + y = 25
[*]3x - y = 20
[/LIST]
Since we have matching opposite coefficients for y (1 and -1), we can add both equations together and eliminate a variable.
(2 + 3)x + (1 - 1)y = 25 + 20
Simplifying, we get:
5x = 45
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D45&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]x = 9[/B]
To find y, we plug in x = 9 into equation (1) or (2). Let's choose equation (1):
2(9) + y = 25
y + 18 = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=y%2B18%3D25&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 7[/B]
So we have (x, y) = (9, 7)
Let's check our work for equation (2) to make sure this system works:
3(9) - 7 ? 20
27 - 7 ? 20
20 = 20 <-- Good, we match!

2 times a number equals that number plus 5

2 times a number equals that number plus 5
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
2 times a number means we multiply 2 by x:
2x
That number plus 5 means we add 5 to the number x
x + 5
The phrase [I]equals[/I] means we set both expressions equal to each other
[B]2x = x + 5[/B] <-- This is our algebraic expression
If you want to take this further and solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3Dx%2B5&pl=Solve']type this expression in the search engine[/URL] and we get:
[B]x = 5[/B]

2 times a number minus 4 times another number is 6. The sum of 2 numbers is 8. Find the 2 numbers

2 times a number minus 4 times another number is 6. The sum of 2 numbers is 8. Find the 2 numbers.
Let the first number be x, and the second number be y. We're given two equations:
[LIST=1]
[*]2x - 4y = 6
[*]x + y = 8
[/LIST]
Using our simultaneous equation calculator, there are 3 ways to solve this:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Substitution']Substitution[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Elimination']Elimination[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
They all give the same answers:
(x, y) = [B](6.3333333, 1.6666667)[/B]

2 times a number subtracted by x

2 times a number subtracted by x
The phrase [I]a number[/I] means an arbitrary variable, let's call it n.
n
2 times a number means we multiply n by 2:
2n
The phrase [I]subtracted by[/I] means we subtract 2n from x:
[B]x - 2n[/B]

2 times as many dimes as quarters and they have a combined value of 180 cents, how many of each coin

2 times as many dimes as quarters and they have a combined value of 180 cents, how many of each coin does he have?
Let d be the number of dimes. Let q be the number of quarters. We're given two equations:
[LIST=1]
[*]d = 2q
[*]0.1d + 0.25q = 180
[/LIST]
Substitute (1) into (2):
0.1(2q) + 0.25q = 180
0.2q + 0.25q = 180
[URL='https://www.mathcelebrity.com/1unk.php?num=0.2q%2B0.25q%3D180&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]q = 400[/B]
Now substitute q = 400 into equation 1:
d = 2(400)
[B]d = 800[/B]

2 times half of a number

A number means an arbitrary variable, let's call it x.
Half of x means we divide x by 2, or multiply by 0.5
x/2
2 times half x is written:
[B]2(x/2)[/B]
If we simplify by cancelling the 2's, we just get x.

2 times the sum of 1 and some number is 30. What is the number?

2 times the sum of 1 and some number is 30. What is the number?
We let the phrase "some number" equal the variable x.
The sum of 1 and some number is:
x + 1
2 times the sum:
2(x + 1)
The word "is" means equal to, so we set [B]2(x + 1) = 30[/B]

2 times the sum of 7 times a number and 4

2 times the sum of 7 times a number and 4
This is an algebraic expression. Let's take it in 4 parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]7 times a number means we multiply x by 7: 7x
[*]The sum of 7 times a number and 4 means we add 4 to 7x: 7x + 4
[*]Finally, we multiply the sum in #3 by 2
[/LIST]
Build our final algebraic expression:
[B]2(7x + 4)[/B]

2 times the sum of a number and 3 is equal to 3x plus 4

2 times the sum of a number and 3 is equal to 3x plus 4
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 3 means we add 3 to x:
x + 3
2 times this sum means we multiply the quantity x + 3 by 2
2(x + 3)
3x plus 4 means 3x + 4 since the word plus means we use a (+) sign
3x + 4
The phrase [I]is equal to[/I] means an equation, where we set 2(x + 3) equal to 3x + 4
[B]2(x + 3) = 3x + 4[/B]

2 times the sum of a number x and 5

2 times the sum of a number x and 5
The sum of a number x and 5 means we add 5 to x:
x + 5
2 times the sum:
[B]2(x + 5)[/B]

2, 4, 6, 8....1000. What term is the number 1000?

2, 4, 6, 8....1000. What term is the number 1000?
Formula for nth term is 2n
If 2n = 1000, then dividing each side by 2, we see that:
2n/2 = 1000/2
n = [B]500[/B]

2/3 of a number 17 is at least 29

2/3 of a number 17 is at least 29
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
2/3 of a number means we multiply x by 2/3:
2x/3
The phrase [I]is at least[/I] also means greater than or equal to, so we set up the inequality:
[B]2x/3 >= 29[/B]

2/5 the cube of a number

2/5 the cube of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The cube of a number means we raise x to the power of 3:
x^3
2/5 of the cube means we multiply x^3 by 2/5:
[B](2x^3)/5[/B]

20 percent of my class is boys. There are 30 boys in class. How many girls in my class

20 percent of my class is boys. There are 30 boys in class. How many girls in my class?
Let c be the number of people in class. Since 20% = 0.2, We're given:
0.2c = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=0.2c%3D30&pl=Solve']Type this equation into our search engine[/URL], we get:
c = 150
Since the class is made up of boys and girls, we find the number of girls in the class by this equation:
Girls = 150 - 30
Girls = [B]120[/B]

20 teachers made a bulk purchase of some textbooks. The teachers received a 24% discount for the bul

20 teachers made a bulk purchase of some textbooks. The teachers received a 24% discount for the bulk purchase, which originally cost $5230. Assuming the cost was divided equally among the teachers, how much did each teacher pay?
[U]Calculate Discount Percent:[/U]
If the teachers got a 24% discount, that means they paid:
100% - 24% = 76%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=76&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']76% as a decimal[/URL] = 0.76 (Discount Percent)
[U]Calculate discount price:[/U]
Discount Price = Full Price * (Discount Percent)
Discount Price = 5230 * 0.76
Discount Price = 3974.80
Price per teacher = Discount Price / Number of Teachers
Price per teacher = 3974.80 / 20
Price per teacher = [B]$198.74[/B]

20% of a number is x. What is 100% of the number? Assume x>0.

20% of a number is x. What is 100% of the number? Assume x>0.
Let the number be n. We're given:
0.2n = x <-- Since 20% = 0.2
To find n, we multiply each side of the equation by 5:
5(0.2)n = 5x
n = [B]5x[/B]

21 apples and 49 pears. What is the largest number of baskets to make and still use up all the fruit

21 apples and 49 pears. What is the largest number of baskets to make and still use up all the fruit
We use our [URL='https://www.mathcelebrity.com/gcflcm.php?num1=21&num2=49&num3=&pl=GCF+and+LCM']greatest common factor calculator for GCF(21, 49)[/URL] to get:
GCF(21, 49) = 7
This means with [B]7 baskets[/B]:
[LIST]
[*]We divide 21 apples by 7 to get 3 apples per basket
[*]We divide 49 pears by 7 to get 7 pears per basket
[/LIST]

21 the total of 21 and

21 the total of 21 and?
Let the number we want be n. We have:
21 = 21 + n
n must be [B]0[/B], since 21 = 21

25 boxes are loaded on a truck. If each box weighs 22 kg, what is the total weight of the load

25 boxes are loaded on a truck. If each box weighs 22 kg, what is the total weight of the load?
Total Weight = Number of boxes * weight per box
Total Weight = 25 * 22 kg
Total Weight = [B]550 kg[/B]

26 increased by 12 times a number

26 increased by 12 times a number
A number is represented by an arbitrary variable, let's call it x
12 times a number is written as 12x
26 increased by 12 times a number means we add:
[B]26 + 12x[/B]

28 less than twice a number

[U]A number means an arbitrary variable, let's call it x.[/U]
[LIST]
[*]x
[/LIST]
[U]Twice a number means multiply by 2[/U]
[LIST]
[*]2x
[/LIST]
[U]28 less than twice a number means we subtract 28[/U]
[LIST]
[*][B]2x - 28[/B]
[/LIST]

28 students in class and 16 are boys what is percent of girls?

28 students in class and 16 are boys what is percent of girls?
Calculate the number of girls:
Girls = Total Students - Boys
Girls = 28 - 16
Girls = 12
The percent of girls is found by this formula:
Percent of Girls = 100 * Number of Girls / Number of Students
Percent of Girls = 100 * 12 / 28
Percent of Girls = 1,200 / 28
Percent of Girls = [B]42.86%[/B]

2x increased by 3 times a number

2x increased by 3 times a number
The phrase [I]a number[/I] means an arbitary variable, let's call it x.
3 times a number means we multiply x by 3:
3x
The phrase [I]increased by[/I] means we add 3x to 2x:
2x + 3x
Simplifying, we get:
[B]5x[/B]

3 boys share 100 in the ratio 1:2:2. how much each boy will get?

3 boys share 100 in the ratio 1:2:2. how much each boy will get?
Given the ratio 1 : 2 : 2, calculate the expected number of items from a population of 100
A ratio of 1 : 2 : 2 means that for every of item A, we can expect 2 of item B and 2 of item c
Therefore, our total group is 1 + 2 + 2 = 5
[SIZE=5][B]Calculate Expected Number of Item A:[/B][/SIZE]
Expected Number of Item A = 1 x 100/5
Expected Number of Item A = 100/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=100&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item A = 20/1
Expected Number of Item A = [B]20[/B]
[SIZE=5][B]Calculate Expected Number of Item B:[/B][/SIZE]
Expected Number of Item B = 2 x 100/5
Expected Number of Item B = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item B = 40/1
Expected Number of Item B = [B]40[/B]
[SIZE=5][B]Calculate Expected Number of Item C:[/B][/SIZE]
Expected Number of Item C = 2 x 100/5
Expected Number of Item C = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item C = 40/1
Expected Number of Item C = [B]40[/B]
[B]Final Answer:[/B]
(A, B, C) =[B] (20, 40, 40)[/B] for 1:2:2 on 100 people

3 decreased by 7 times a number

3 decreased by 7 times a number
A number signifies an arbitrary variable, let's call it x.
7 times a number:
7x
3 decreased by this means we subtract 7x
[B]3 - 7x[/B]

3 is subtracted from square of a number

3 is subtracted from square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Square of a number means we raise x to the 2nd power:
x^2
3 is subtracted from square of a number
[B]x^2 - 3[/B]

3 less than a number times itself

3 less than a number times itself
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Itself means the same variable as above. So we have:
x * x
x^2
3 less than this means we subtract 3 from x^2:
[B]x^2 - 3[/B]

3 more than the product of 7 and a number x is less than 26

The product of 7 and a number x is written as 7x.
3 more than that product is written as 7x + 3.
Finally, that entire expression is less than 26, so we have:
7x + 3 < 26 as our algebraic expression.

3 people can build a shed in 8 hours, how long would it take 5 people

3 people can build a shed in 8 hours, how long would it take 5 people
We set up a proportion of people to hours where h is the number of hours for 5 people:
3/8 = 5/h
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=5&den1=8&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']Using our proportion calculator[/URL], we get:
13.3333 hours
But what if the problem asks for minutes? Then we say 8 hours = 60 * 8 = 480 minutes. We set up the proportion where m is the number of minutes:
3/480 = 5/m
In this case, [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=5&den1=480&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']we use our search engine again[/URL] and get:
m = 800

3 times a number increased by 1 is between -8 and 13

3 times a number increased by 1 is between -8 and 13.
Let's take this algebraic expression in [U]4 parts[/U]:
Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Part 2 - 3 times this number means we multiply x by 3:
3x
Part 3 - Increased by 1 means we add 1 to 3x:
3x + 1
The phrase [I]between[/I] means we have an inequality:
[B]-8 <= 3x + 1 <=13[/B]

3 times a number is 3 more a number

3 times a number is 3 more a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
3 times a number:
3x
3 more than a number means we add 3 to x:
x + 3
The word [I]is[/I] means and equation, so we set 3x equal to x + 3
[B]3x = x + 3[/B]

3 times the square of a number x minus 12

3 times the square of a number x minus 12.
Build the algebraic expression piece by piece:
[LIST]
[*]Square of a number x: x^2
[*]3 times this: 3x^2
[*]Minus 12: [B]3x^2 - 12[/B]
[/LIST]

3, 8, 13, 18, .... , 5008 What term is the number 5008?

3, 8, 13, 18, .... , 5008 What term is the number 5008?
For term n, we have a pattern:
f(n) = 5(n - 1) + 3
Set this equal to 5008
5(n - 1) + 3 = 5008
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=5%28n-1%29%2B3%3D5008&pl=Solve']equation solver,[/URL] we get:
n = [B]1002[/B]

3/4 a number b divided by 5

3/4 a number b divided by 5
3/4 a number b:
3b/4
Divided by 5:
3b/4/5
We multiply top and bottom by 5 to remove the double fraction:
3b*5/4
[B]15b/4[/B]

3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the

3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the program, how many workers are employed at this company?
We read this as 3/5 of the total workers employed at the company equals 24. Let w be the number of workers. We have the following equation:
3/5w = 24
Run [URL='http://www.mathcelebrity.com/1unk.php?num=3%2F5w%3D24&pl=Solve']3/5w = 24[/URL] through the search engine, we get [B]w = 40[/B].

30 increased by 3 times the square of a number

Let "a number" equal the arbitrary variable x.
The square of that is x^2.
3 times the square of that is 3x^2.
Now, 30 increased by means we add 3x^2 to 30
30 + 3x^2

30 increased by 3 times the square of a number

30 increased by 3 times the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The square of a number means we raise x to the power of 2:
x^2
3 times the square:
3x^2
The phrase [I]increased by[/I] means we add 3x^2 to 30:
[B]30 + 3x^2[/B]

32 girls and 52 boys were on an overseas learning trip . They were divided into as many groups as po

32 girls and 52 boys were on an overseas learning trip . They were divided into as many groups as possible where the number of groups of girls and the number of groups of boys is the same .how many boys and how many girls were in each group
We want a number such that our total members divided by this number equals our group size.
We take the greatest common factor (32,52) = 4
Therefore, we have:
[LIST]
[*][B]32/4 = 8 girls in each group[/B]
[*][B]52/4 = 13 boys in each group[/B]
[/LIST]

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many s

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?
The number of students who went on the bus is 331 - 7 in the car = 324
324 students on the bus / 6 buses = [B]54 per bus[/B]

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many s

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?
Calculate the students in buses:
Students in buses = Total Students - Students in Cars
Students in buses = 331 - 7
Students in buses = 324
Calculate the students in each bus
Students in each bus = Students in buses / Number of Buses
Students in each bus = 324 / 6
Students in each bus = [B]54[/B]

38 books into 8 boxes. 6 left. How many books in each box

38 books into 8 boxes. 6 left. How many books in each box
Let the number of books in each box be b. We have the following relation:
8b + 6 = 38
to solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B6%3D38&pl=Solve']type it in our search engine[/URL] and we get:
b = [B]4[/B]

3timesanumberdecreasedby3

A necklace chain costs $15. Beads cost $2.50 each. You spend a total of $30 on a necklace and beads before tax. How many beads did you buy in addition to the necklace?
Let the number of beads be b. We're given the following equation:
2.5b + 15 = 30
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5b%2B15%3D30&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]6[/B]

4 adults and 3 children cost $40. Two adults and 6 children cost $38

4 adults and 3 children cost $40. Two adults and 6 children cost $38
Givens and Assumptions:
[LIST]
[*]Let the number of adults be a
[*]Let the number of children be c
[*]Cost = Price * Quantity
[/LIST]
We're given 2 equations:
[LIST=1]
[*]4a + 3c = 40
[*]2a + 6c = 38
[/LIST]
We can solve this system of equations 3 ways
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we use, we get:
[LIST]
[*][B]a = 7[/B]
[*][B]c = 4[/B]
[/LIST]

4 machines can complete a job in 6 hours how long will it take 3 machines to complete the same jobs?

4 machines can complete a job in 6 hours how long will it take 3 machines to complete the same jobs?
Set up a proportion of machines to hours where h is the number of hours that 3 machines take:
4/6 = 3/h
[URL='https://www.mathcelebrity.com/prop.php?num1=4&num2=3&den1=6&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get:
h = [B]4.5[/B]

4 teaspons of vegetable oil and 6 teaspoons of vinegar. 20 teaspoons of vegetable oil to how many te

4 teaspons of vegetable oil and 6 teaspoons of vinegar. 20 teaspoons of vegetable oil to how many teaspoons of vinegar?
Set up a proportion where x is the number of teaspoons of vinegar in the second scenario:
4/6 = 20/x
[URL='http://www.mathcelebrity.com/prop.php?num1=4&num2=20&den1=6&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']Plug that expression into the search engine to get[/URL]
[B]x = 30[/B]

4 times a number added to 8 times a number equals 36

4 times a number added to 8 times a number equals 36
Let [I]a number[/I] be an arbitrary variable, let us call it x.
4 times a number:
4x
8 times a number:
8x
We add these together:
4x + 8x = 12x
We set 12x equal to 36 to get our final algebraic expression of:
[B]12x = 36
[/B]
If the problem asks you to solve for x, you [URL='https://www.mathcelebrity.com/1unk.php?num=12x%3D36&pl=Solve']type this algebraic expression into our search engine[/URL] and get:
x = [B]3[/B]

4 times a number cubed decreased by 7

4 times a number cubed decreased by 7
A number is denoted as an arbitrary variable, let's call it x
x
Cubed means raise x to the third power
x^3
Decreased by 7 means subtract 7
x^3 - 7

4 times a number is the same as the number increased by 78

4 times a number is the same as the number increased by 78.
Let's take this algebraic expression in parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]4 times a number is written as 4x
[*]The number increased by 78 means we add 78 to x: x + 78
[*]The phrase [I]the same as[/I] mean an equation, so we set #2 equal to #3
[/LIST]
[B]4x = x + 78[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further, then [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3Dx%2B78&pl=Solve']we type this equation into our search engine [/URL]and get:
x = 26

4 times a number plus 9

A number means an arbitrary variable, let's call it "x".
4 times a number is 4x.
Plus 9 means we add:
4x + 9

4 times the difference of 6 times a number and 7

4 times the difference of 6 times a number and 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
6 times a number
6x
The difference of 6x and 7 means we subtract 7 from 6x:
6x - 7
Now we multiply this difference by 4:
[B]4(6x - 7)[/B]

4 times the number of cows plus 2 times the number of ducks

4 times the number of cows plus 2 times the number of ducks
Let c be the number of cows. Let d be the number of ducks. We've got an algebraic expression below:
[B]4c + 2d[/B]

4 times the quantity of a number plus 6

4 times the quantity of a number plus 6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The word [I]plus[/I] means we addd 6 to x
x + 6
The phrase [I]4 times the quantity [/I]means we multiply x + 6 by 4
[B]4(x + 6)[/B]

414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost wa

414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost was $755.25. How many adults and children used the pool
Let the number of children who used the pool be c, and the number of adults who used the pool be a. We're given two equations:
[LIST=1]
[*]a + c = 414
[*]2a + 1.75c = 755.25
[/LIST]
We have a simultaneous equations. You can solve this any of 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
Whichever method you choose, you get the same answer:
[LIST]
[*][B]a = 123[/B]
[*][B]c = 291[/B]
[/LIST]

45 students, 12 taking spanish, 15 taking chemistry, 5 taking both spanish and chemistry. how many s

45 students, 12 taking spanish, 15 taking chemistry, 5 taking both spanish and chemistry. how many students are not taking either?
Let S be the number of students taking spanish and C be the number of students taking chemistry:
We have the following equation relating unions and intersections:
P(C U S) = P(C) + P(S) - P(C and S)
P(C U S) = 15 + 12 - 5
P(C U S) = 22
To get people that aren't taking either are, we have:
45 - P(C U S)
45 - 22
[B]23[/B]

45 water balloons were given to 9 children. If each child received the same number of water balloons

45 water balloons were given to 9 children. If each child received the same number of water balloons, how many water balloons did each child receive?
Water Balloons per child = Total Water Balloons / Number of Children
Water Balloons per child = 45/9
Water Balloons per child = [B]5[/B]

46 people showed up to the party. There were 8 less men than women present. How many men were there?

46 people showed up to the party. There were 8 less men than women present. How many men were there?
Let the number of men be m. Let the number of women be w. We're given two equations:
[LIST=1]
[*]m = w - 8 [I](8 less men than women)[/I]
[*]m + w = 46 [I](46 showed up to the party)[/I]
[/LIST]
Substitute equation (1) into equation (2) for m:
w - 8 + w = 46
To solve for w in this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=w-8%2Bw%3D46&pl=Solve']type in the equation into our search engine [/URL]and we get:
w = 27
To solve for men (m), we substitute w = 27 into equation (1):
m = 27 - 8
m = [B]19[/B]

4subtractedfrom6timesanumberis32

4 subtracted from 6 times a number is 32.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
6 times this number means we multiply by x by 6
6x
4 subtracted from this expression means we subtract 4
6x - 4
The phrase [I]is[/I] means an equation, so we set 6x - 4 equal to 32
[B]6x - 4 = 32
[/B]
If you need to solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=6x-4%3D32&pl=Solve']type it in the search engine here[/URL].

5 is one-fourth of a number c

5 is one-fourth of a number c
[LIST]
[*]A number c is just written as c
[*]one-fourth of c means we multiply c by 1/4: c/4
[*]The phrase [I]is[/I] means equal to, so we set c/4 equal to 5
[/LIST]
[B]c/4 = 5[/B]

5 more than the reciprocal of a number

5 more than the reciprocal of a number
Take this algebraic expression in pieces:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of this number means we divide 1 over x:
1/x
5 more means we add 5 to 1/x
[B]1/x + 5[/B]

5 more than twice the cube of a number

5 more than twice the cube of a number.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The cube of a number means we raise it to a power of 3
x^3
Twice the cube of a number means we multiply x^3 by 2
2x^3
5 more than twice the cube of a number means we multiply 2x^3 by 5
5(2x^3)
Simplifying, we get:
10x^3

5 more than twice the cube of a number

5 more than twice the cube of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The cube of a number means we raise x to the power of 3:
x^3
Twice the cube means we multiply x^3 by 2
2x^3
Finally, 5 more than twice the cube means we add 5 to 2x^3:
[B]2x^3 + 5[/B]

5 squared minus a number x

5 squared minus a number x
5 squared is written as 5^2
Minus a number x means we subtract the variable x
[B]5^2 - x[/B]

5 subtracted from 3 times a number is 44

5 subtracted from 3 times a number is 44.
The problem asks for an algebraic expression.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
3 times this number is 3x.
5 subtracted from this is written as 3x - 5.
The phrase [I]is[/I] means an equation, so we set 3x - 5 equal to 44
[B]3x - 5 = 44[/B]

5 times a number increased by 13

5 times a number increased by 13
A number is denoted as an arbitrary variable, let's call it x
x
5 times that number
5x
Increased by 13 means we add
5x + 13

5 times a number increased by 4 is divided by 6 times the same number

5 times a number increased by 4 is divided by 6 times the same number
Take this algebraic expression in parts.
Part 1: 5 times a number increased by 4
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x
[*]5 times the number means multiply x by 5: 5x
[*][I]Increased by 4[/I] means we add 4 to 5x: 5x + 4
[/LIST]
Part 2: 6 times the same number
[LIST]
[*]From above, [I]a number[/I] is x: x
[*]6 times the number means we multiply x by 6: 6x
[/LIST]
The phrase [I]is divided by[/I] means we have a quotient, where 5x + 4 is the numerator, and 6x is the denominator.
[B](5x + 4)/6x[/B]

5 times a number is 4 more than twice a number

5 times a number is 4 more than twice a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
5 times a number:
5x
Twice a number means we multiply x by 2:
2x
4 more than twice a number
2x + 4
The word [I]is[/I] means equal to, so we set 5x equal to 2x + 4
[B]5x = 2x + 4[/B]

5 times a number is that number minus 3

5 times a number is that number minus 3
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[LIST]
[*]5 times a number: 5x
[*]That number means we use the same number from above which is x
[*]That number minus 3: x - 3
[*]The phrase [I]is[/I] means an equation, so we set 5x equal to x - 3
[/LIST]
[B]5x = x - 3[/B]

5 times the product of 2 numbers a and b

5 times the product of 2 numbers a and b
The product of 2 numbers a and be means we multiply the variables together:
ab
5 times the product means we multiply ab by 5:
[B]5ab[/B]

5 times the sum of 3 times a number and -5

5 times the sum of 3 times a number and -5
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
3 times a number means we multiply x by 3:
3x
the sum of 3 times a number and -5 means we add -5 to 3x:
3x - 5
5 times the sum means we multiply 3x - 5 by 5:
[B]5(3x - 5)[/B]

5, 14, 23, 32, 41....1895 What term is the number 1895?

5, 14, 23, 32, 41....1895 What term is the number 1895?
Set up a point slope for the first 2 points:
(1, 5)(2, 14)
Using [URL='https://www.mathcelebrity.com/search.php?q=%281%2C+5%29%282%2C+14%29&x=0&y=0']point slope formula, our series function[/URL] is:
f(n) = 9n - 4
To find what term 1895 is, we set 9n - 4 = 1895 and solve for n:
9n - 4 = 1895
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=9n-4%3D1895&pl=Solve']equation solver[/URL], we get:
n = [B]211[/B]

5,10,15,20 What is the next number? What is the 100th term?

5,10,15,20
What is the next number?
What is the 100th term?
Increment is by 5, so next number is 20 + 5 = [B]25[/B]
Formula for nth number is 5 * n
With n = 100, we have 5 * 100 = [B]500[/B]

5000 union members of a financially troubled company accepted a 17% pay cut. The company announced t

5000 union members of a financially troubled company accepted a 17% pay cut. The company announced that this would save them approximately $108 million annually. Based on this information, calculate the average annual pay of a single union member
Let the full salary of the union members be s. Since 17% is 0.17, We're given:
0.17s = 108000000
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.17s%3D108000000&pl=Solve']type it in our search engine[/URL] and we get:
s = 635,294,117.65
Calculate the average annual pay of a single union member:
Average Pay = Total Pay / Number of Union Members
Average Pay = 635,294,117.65 / 5000
Average Pay = [B]127,058.82[/B]

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $885.50. How many kids and how many adults were there?
Assumptions:
[LIST]
[*]Let the number of adults be a
[*]Let the number of kids be k
[/LIST]
Given with assumptions:
[LIST=1]
[*]a + k = 508
[*]2a + 1.25k = 885.50 (since cost = price * quantity)
[/LIST]
Rearrange equation (1) by subtracting c from each side to isolate a:
[LIST=1]
[*]a = 508 - k
[*]2a + 1.25k = 885.50
[/LIST]
Substitute equation (1) into equation (2):
2(508 - k) + 1.25k = 885.50
Multiply through:
1016 - 2k + 1.25k = 885.50
1016 - 0.75k = 885.50
To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=1016-0.75k%3D885.50&pl=Solve']type this equation into our search engine[/URL] and we get:
k = [B]174[/B]
Now, to solve for a, we substitute k = 174 into equation 1 above:
a = 508 - 174
a = [B]334[/B]

51 decreased by twice a number

A number is denoted as an arbitrary variable, let's call it x.
Twice a number means we multiply by 2, so 2x.
51 decreased by twice a number means we subtract 2x from 51
[B]51 - 2x[/B]

6 is divided by square of a number

6 is divided by square of a number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
x
the square of this means we raise x to the power of 2:
x^2
Next, we divide 6 by x^2:
[B]6/x^2[/B]

6 is one third of a number s

6 is one third of a number s
A number s is written as s:
s
One third of a number s means we multiply s by 1/3
s/3
The word [I]is[/I] means equal to, so we set s/3 equal to 6
[B]s/3 = 6[/B]

6 numbers have a mean of 4. What is the total of the 6 numbers?

6 numbers have a mean of 4. What is the total of the 6 numbers?
Mean = Sum of numbers / Count of numbers
Plug our Mean of 4 and our count of 6 into this equation:
4 = Sum/Total of Numbers / 6
Cross multiply:
Sum/Total of Numbers = 6 * 4
Sum/Total of Numbers = [B]24[/B]

6 plus twice the sum of a number and 7.

6 plus twice the sum of a number and 7.
The phrase [I]a number[/I] mean an arbitrary variable, let's call it x.
The sum of a number and 7 means we add 7 to the variable x.
x + 7
Twice the sum means we multiply the sum by 2:
2(x + 7)
6 plus means we add 6 to 2(x + 7)
[B]6 + 2(x + 7)[/B]

6 sided die probability to roll a odd number or a number less than 6

6 sided die probability to roll a odd number or a number less than 6
First, we'll find the set of rolling an odd number. [URL='https://www.mathcelebrity.com/1dice.php?gl=1&opdice=1&pl=Odds&rolist=+2%2C3%2C4&dby=+2%2C3%2C5&montect=+100']From this dice calculator[/URL], we get:
Odd = {1, 3, 5}
Next, we'll find the set of rolling less than a 6. [URL='https://www.mathcelebrity.com/1dice.php?gl=4&pl=6&opdice=1&rolist=+2%2C3%2C4&dby=+2%2C3%2C5&montect=+100']From this dice calculator[/URL], we get:
Less than a 6 = {1, 2, 3, 4, 5}
The question asks for [B]or[/B]. Which means a Union:
{1, 3, 5} U {1, 2, 3, 4, 5} = {1, 2, 3, 4, 5}
This probability is [B]5/6[/B]

6 subtracted from the product of 5 and a number is 68

6 subtracted from the product of 5 and a number is 68
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The product of 5 and this number is:
5x
We subtract 6 from 5x:
5x - 6
The phrase [I]is[/I] means an equation, so we set 5x - 6 equal to 68
[B]5x - 6 = 68[/B]

6 times a number multiplied by 3 all divided by 4

6 times a number multiplied by 3 all divided by 4
Take this algebraic expression in parts:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]6 times a number: 6x
[*]Multiplied by 3: 3(6x) = 18x
[*]All divided by 4: 18x/4
[/LIST]
We can simplify this:
We type 18/4 into our search engine, simplify, and we get 9/2. So our answer is:
[B]9x/2[/B]

6 times a number, x, is at least 22.

6 times a number, x, is at least 22.
6 times a number x:
6x
The phrase [I]is at least[/I] means greater than or equal to. So we have an inequality:
[B]6x >= 22[/B] <-- This is our algebraic expression
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6x%3E%3D22&pl=Show+Interval+Notation']To solve this for x, paste this into the search engine[/URL] and we get:
[B]x >= 3.666667[/B]

6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number

6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number
We've got two algebraic expressions here. Let's take it in parts:
Term 1:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The reciprocal is 1/x
Multiply this by 6: 6/x
Term 2:
Reciprocal of 7: 1/7
2 times this: 2/7
We set these terms equal to each other:
6/x = 2/7
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=2&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get:
[B]x = 21[/B]

6 times the reciprocal of a number equals 3 times the reciprocal of 7 .

6 times the reciprocal of a number equals 3 times the reciprocal of 7 .
This is an algebraic expression. Let's take it in parts:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of a number x means we divide 1 over x:
1/x
6 times the reciprocal means we multiply 6 by 1/x:
6/x
The reciprocal of 7 means we divide 1/7
1/7
3 times the reciprocal means we multiply 1/7 by 3:
3/7
Now, the phrase [I]equals[/I] mean an equation, so we set 6/x = 3/7
[B]6/x = 3/7[/B] <-- This is our algebraic expression
If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=3&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']we type this proportion in our search engine[/URL] and get:
x = 14

6 times the sum of a number and 3 is equal to 42. What is this number?

6 times the sum of a number and 3 is equal to 42. What is this number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The sum of a number and 3 means we add 3 to x:
x + 3
6 times the sum:
6(x + 3)
The word [I]is[/I] means an equation, so we set 6(x + 3) equal to 42 to get our [I]algebraic expression[/I] of:
[B]6(x + 3) = 42[/B]
[B][/B]
If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/1unk.php?num=6%28x%2B3%29%3D42&pl=Solve']you type this equation into our search engine[/URL] and you get:
x = [B]4[/B]

6 times the sum of a number and 5 is 16

6 times the sum of a number and 5 is 16
A number represents an arbitrary variable, let's call it x
x
The sum of x and 5
x + 5
6 times the sum of x and 5
6(x + 5)
Is means equal to, so set 6(x + 5) equal to 16
[B]6(x + 5) = 16[/B]

60 percent of a number minus 17 is -65

60 percent of a number minus 17 is -65
Using our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=60&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percent to decimal calculator[/URL], we see that 60% is 0.6, so we have:
0.6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So 60% of a number is:
0.6x
Minus 17:
0.6x - 17
The word [I]is[/I] means an equation, so we set 0.6x - 17 equal to -65 to get our algebraic expression of:
[B]0.6x - 17 = -65[/B]
[B][/B]
If you want to solve for x in this equation, you [URL='https://www.mathcelebrity.com/1unk.php?num=0.6x-17%3D-65&pl=Solve']type it in our search engine and you get[/URL]:
[B]x = -80[/B]

7 black shirts 5 white shirts 10 gray shirts one is chosen at random, what is the probability that i

7 black shirts 5 white shirts 10 gray shirts one is chosen at random, what is the probability that it is not gray
[U]Find the total shirts:[/U]
Total shirts = Black Shirts + White Shirts + Gray Shirts
Total shirts = 7 + 5 + 10
Total shirts = 22
[U]Calculate the probability of choosing a gray shirt:[/U]
P(Gray) = Number of Gray shirts / Total Shirts
P(Gray) = 10/22
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=10%2F22&frac2=3%2F8&pl=Simplify']type in 10/22 into our search engine, choose simplify[/URL], and we get:
P(Gray) = [B]5/11[/B]

7 is 1/4 of some number

7 is 1/4 of some number
The phrase [I]some number[/I] means an arbitrary variable, let's call it x.
1/4 of this is written as:
x/4
The word [I]is[/I] means an equation, so we set x/4 equal to 7:
[B]x/4 = 7[/B]

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is written as -2x.
Less means subtract, so we have 7 less than this is -2x - 7.
Finally, greater than or equal to is >=, so our expression becomes:
-2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is denoted as -2x.
7 less than that means we subtract 7:
-2x - 7
Finally, that entire expression is greater than or equal to 41
-2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is denoted as -2x.
7 less means we subtract, so 7 less than that is -2x - 7.
Finally, that entire expression is greater than or equal to 41
-2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41

7 less than -2 times a number x is greater than or equal to 41
-2 times a number x
-2x
7 less than this
-2x - 7
Now we set this expressions greater than or equal to 41
[B]-2x - 7 >= 41[/B]

7 minus a number all divided by 4

7 minus a number all divided by 4
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
7 minus a number
7 - x
All divided by 4:
[B](7 - x)/4[/B]

7 out of every 30 students ride their bikes to school. There are 720 students. How many ride their b

7 out of every 30 students ride their bikes to school. There are 720 students. How many ride their bikes
Set up a proportion of students who ride their bike to total students where r is the number of students who ride their bikes:
7/30 = r/720
To solve this proportion for r, we [URL='https://www.mathcelebrity.com/prop.php?num1=7&num2=r&den1=30&den2=720&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our calculation engine and we get:[/URL]
r = [B]168[/B]

7 plus the quantity of 9 increased by a number

7 plus the quantity of 9 increased by a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
9 increased by a number means we add 9 to x
9 + x
7 plus this quantity means we add (9 + x) to 7
[B]7 + (9 + x)[/B]

7 times a number and 2 is equal to 4 times a number decreased by 8

7 times a number and 2 is equal to 4 times a number decreased by 8
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
7 times a number:
7x
and 2 means we add 2:
7x + 2
4 times a number
4x
decreased by 8 means we subtract 8:
4x - 8
The phrase [I]is equal to[/I] means an equation, so we set 7x + 2 equal to 4x - 8:
[B]7x + 2 = 4x - 8[/B]

7 times a number increased by 4 times the number

7 times a number increased by 4 times the number
Let [I]a number[/I] and [I]the number[/I] be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:
[LIST]
[*]7 times a number: 7x
[*]4 times the number: 4x
[*]The phrase [I]increased by[/I] means we add 4x to 7x:
[*]7x + 4x
[*]Simplifying, we get: (7 + 4)x
[*][B]11x[/B]
[/LIST]

7 times a number is the same as 12 more than 3 times a number

7 times a number is the same as 12 more than 3 times a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[B][U]Algebraic Expression 1:[/U][/B]
7 times a number means we multiply 7 by x:
7x
[B][U]Algebraic Expression 2:[/U][/B]
3 times a number means we multiply 3 by x:
3x
12 more than 3 times a number means we add 12 to 3x:
3x + 12
The phrase [I]is the same as[/I] means an equation, so we set 7x equal to 3x + 12
[B]7x = 3x + 12[/B] <-- Algebraic Expression

7 times a positive number n is decreased by 3, it is less than 25

7 times a positive number n is decreased by 3, it is less than 25
7 times a positive number n:
7n
Decreased by 3:
7n - 3
The phrase [I]it is less than [/I]means an inequality. So we relate 7n - 3 less than 25 using the < sign to get our algebraic expression of:
[B]7n - 3 < 25[/B]

7 times the number of lions plus 4 times the number of tigers

7 times the number of lions plus 4 times the number of tigers
Let the number of lions be l
Let the number of tigers be t
We have an algebraic expression of:
[B]7l + 4t[/B]

7 times the quantity of 3 times a number reduced by 10

7 times the quantity of 3 times a number reduced by 10
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
3 times a number:
3x
Reduced by 10 means we subtract 10:
3x - 10
7 times this quantity:
[B]7(3x - 10)[/B]

7, 10, 15, 22 What is the next number in the sequence? What is the 500th term?

7, 10, 15, 22
What is the next number in the sequence?
What is the 500th term?
We see that:
1^2 + 6 = 7
2^2 + 6 = 10
3^3 + 6 = 15
4^2 + 6 = 22
We build our function as f(n) = n^2 + 6
Next term in the sequence is f(5)
f(5) = 5^2 + 6
f(5) = 25 + 6
f(5) = [B]31
[/B]
Calculate the 500th term:
f(500) = 500^2 + 6
f(500) = 250,000 + 6
f(500) = [B]250,006[/B]

72 pounds and increases by 3.9 pounds per month

72 pounds and increases by 3.9 pounds per month
Let m be the number of months. We write the algebraic expression below:
[B]3.9m + 72[/B]

76 decreased by twice a number. Use the variable n to represent the unknown number

76 decreased by twice a number. Use the variable n to represent the unknown number.
Twice a number (n) means we multiply the unknown number n by 2:
2n
76 decreased by twice a number means we subtract 2n from 76 using the (-) operator
[B]76 - 2n[/B]

8 bags weigh 14 pounds. how much do 20 bags weigh

8 bags weigh 14 pounds. how much do 20 bags weigh
Set up a proportion of bags to pounds where p is the number of pounds for 20 bags:
8/14 = 20/p
We [URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=20&den1=14&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion in our calculator[/URL] and we get:
p = [B]35[/B]

8 increased by the product of a number and 7 is greater than or equal to -18

Take this in parts:
First, the phrase, "a number" means we pick an arbitrary variable, let's call it x.
The product of a number and 7 is 7x.
8 increased by the product of 7x means we add them together.
7x + 8
Finally that entire expression is greater than [U]or equal to[/U] -18
[B]7x + 8 >=-18[/B]

8 is subtracted from thrice a number

Thrice a number means we multiply by 3. A number means an arbitrary variable, let's call it x
3x
8 is subtracted from 3x
[B]3x - 8[/B]

8 is subtracted from twice a number

Twice a number:
[LIST]
[*]Choose an arbitrary variable, let's call it x
[*]Twice x means multiply by 2
[*]2x
[/LIST]
8 subtracted from 2x:
[B]2x - 8[/B]

8 more than twice a number is less than 6 more than the number

8 more than twice a number is less than 6 more than the number.
This is an algebraic expression, let's take it in pieces...
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
8 more than twice a number:
Twice a number means multiply x by 2: 2x
Then add 8: 2x + 8
6 more than the number, means we add 6 to x
x + 6
The phrase [I]is less than[/I] means an inequality, where we set 2x + 8 less than x + 6
[B]2x + 8 < x + 6[/B]

8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is

8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is the number?
Let the number be n. We're given two expressions:
[LIST=1]
[*]8(n - 2) [I]difference means we subtract[/I]
[*]3(n + 3) [I]sum means we add[/I]
[/LIST]
The phrase [I]is the same as[/I] mean an equation. So we set the first expression equal to the second expression:
8(n - 2) = 3(n + 3)
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=8%28n-2%29%3D3%28n%2B3%29&pl=Solve']type it in our search engine[/URL] and we see that:
n =[B] 5[/B]

8 times the sum of 5 times a number and 9

8 times the sum of 5 times a number and 9
Take this algebraic expression in parts:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
5 times a number means:
5x
The sum of this and 9 means we add 9 to 5x:
5x + 9
Now we multiply 8 times this sum:
[B]8(5x + 9)[/B]

8,11,14,17,20 What is the next number? What is the 150th term?

8,11,14,17,20
What is the next number?
What is the 150th term?
We're adding by 3 to the last number in the sequence, so we have the next number as:
20 + 3 = [B]23
[/B]
For the nth term, we have a formula of this:
3n + 5
3(1) + 5 = 8
3(2) + 5 = 11
3(3) + 5 = 14
With n = 150, we have:
3(150) + 5 = 450 + 5 = [B]455[/B]

80 people 40% were women 12 were children. How many men?

80 people 40% were women 12 were children. How many men?
Calculate the number of women:
40% of 80 is 32.
12 were children, so the women and children = 32 + 12 = 44.
Which means the men = 80 - 44 = [B]36[/B]

9 friends were paid $385 to clean up the local lake. How much does each friend receive

9 friends were paid $385 to clean up the local lake. How much does each friend receive
Each friend gets:
Total Payment / Number of friends
$385/9
[B]$42.78[/B]

9 is one-third of a number x

9 is one-third of a number x
A number x can be written as x
x
one-third of a number x means we multiply x by 1/3:
x/3
The phrase [I]is[/I] means an equation, so we set 9 equal to x/3 to get our final algebraic expression of:
[B]x/3 = 9[/B]
If the problem asks you to solve for x, you [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=9&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type this algebraic expression into our search engine[/URL] and you get:
[B]x = 27[/B]

9 is the sum of 7 and twice a number

9 is the sum of 7 and twice a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Twice a number means we multiply x by 2:
2x
The sum of 7 and twice a number
7 + 2x
The word [I]is[/I] mean equal to, so we set 7 + 2x equal to 9:
[B]7 + 2x = 9[/B]

9 less than 5 times a number is 3 more than 2x

9 less than 5 times a number is 3 more than 2x
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
5 times a number means we multiply x by 5:
5x
9 less than 5x means we subtract 9 from 5x:
5x - 9
3 more than 2x means we add 3 to 2x:
2x + 3
The word [I]is[/I] means an equation, so we set 5x - 9 equal to 2x + 3:
[B]5x - 9 = 2x + 3 <-- This is our algebraic expression[/B]
[B][/B]
If you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-9%3D2x%2B3&pl=Solve']type this equation into the search engine[/URL], and we get:
x = [B]4[/B]

9 subtracted from the product of 3 and a number is greater than or equal to 16

9 subtracted from the product of 3 and a number is greater than or equal to 16
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The product of 3 and a number means we multiply 3 times x: 3x
[*]9 subtracted from the product: 3x - 9
[*]The phrase is greater than or equal to means an inequality. So we set up an inequality with >= for the greater than or equal to sign in relation to 3x - 9 and 16
[/LIST]
Our algebraic expression (inequality) becomes:
[B]3x - 19 >= 16[/B]

9 times a number is that number minus 10

9 times a number is that number minus 10
The phrase [I]a number[/I] means we define a random/arbitrary variable, let's call it x:
x
9 times a number means we multiply x by 9:
9x
The phrase [I]that number[/I] refers back to the original arbitrary variable we defined above, which is x:
x
That number minus 10 means we subtract 10 from x:
x - 10
The word [I]is[/I] means equal to, so we set 9x equal to x - 10
[B]9x = x - 10[/B]

9 times a number is that number minus 3

9 times a number is that number minus 3
Let [I]a number[/I] be an arbitrary variable, let's call it x. We're given:
9 times a number is 9x
The number minus 3 is x - 3
The word [I]is[/I] means an equation, so we set 9x equal to x - 3 to get our [I]algebraic expression[/I]:
[B]9x = x - 3[/B]
To solve for x, we type this equation into our search engine and we get:
x = [B]-0.375 or -3/8[/B]

9, 3, 1, 1/3, 1/9 What is the next number in this sequence? What is the function machine for this se

9, 3, 1, 1/3, 1/9
What is the next number in this sequence?
What is the function machine for this sequence?
We see the following pattern in this sequence:
9 = 9/3^0
3 = 9/3^1
1 = 9/3^2
1/3 = 9/3^3
1/9 = 9/3^4
Our function machine formula is:
[B]f(n) = 9/3^(n - 1)
[/B]
Next term is the 6th term:
f(6) = 9/3^(6 - 1)
f(6) = 9/3^5
f(6) = 9/243
f(6) = [B]1/27[/B]

993 cold drinks bottles are to be placed in crates. Each crate can hold 9 bottles. How many crates w

993 cold drinks bottles are to be placed in crates. Each crate can hold 9 bottles. How many crates would be needed and how many bottles will remain?
Let c equal the number of crates
9 bottles per crate * c = 993
9c = 993
Solve for [I]c[/I] in the equation 9c = 993
[SIZE=5][B]Step 1: Divide each side of the equation by 9[/B][/SIZE]
9c /9 = 993/9
c = 110.33333333333
Since we can't have fractional crates, we round up 1 to the next full crate
c = [B]111[/B]

A $1,000 investment takes a 10% loss each year. What will be the value 3 years?

A $1,000 investment takes a 10% loss each year. What will be the value 3 years?
10% is 0.1. Our Balance function B(y) where y is the number of years since the start is:
B(y) = 1000(1 - 0.1)^y
B(y) = 1000(0.9)^y
We want to know B(3):
B(3) = 1000(0.9)^3
B(3) = 1000(0.729)
B(3) = [B]729[/B]

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and short response questions are worth 8 points each. Write a system of linear equations that represents this situation
Assumptions:
[LIST]
[*]Let m be the number of multiple choice questions
[*]Let s be the number of short response questions
[/LIST]
Since total points = points per problem * number of problems, we're given 2 equations:
[LIST=1]
[*][B]m + s = 20[/B]
[*][B]3m + 8s = 100[/B]
[/LIST]
We can solve this system of equations 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[B]m = 12, s = 8[/B]

a 12 sided die is rolled find the probability of rolling a number greater than 7

a 12 sided die is rolled find the probability of rolling a number greater than 7
We assume this is a fair die, not loaded.
This means each side 1-12 has an equal probability of 1/12 of being rolled.
The problem asks, P(Roll > 7)
Greater than 7 means our sample space is {8, 9, 10, 11, 12}
If each of these 5 faces have an equal probability of being rolled, then we have:
P(Roll > 7) = P(Roll = 8) + P(Roll = 9) + P(Roll = 10) + P(Roll = 11) + P(Roll = 12)
P(Roll > 7) = 1/12 + 1/12 + 1/12 + 1/12 + 1/12
P(Roll > 7) =[B] 5/12[/B]

A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12}. Find t

A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12}. Find the probability of rolling a number less than 6.
We have 12 outcomes.
Less than 6 means 1, 2, 3, 4, 5.
Our probability P(x < 6) is:
P(x < 6) = [B]5/12[/B]

A 16 pound roast will feed 24 people. If the largest roast you can buy is 12 pounds. How many people

A 16 pound roast will feed 24 people. If the largest roast you can buy is 12 pounds. How many people can you feed?
Set up a proportion of roast pounds to people fed, where p is the number of people fed on a 12 pound roast:
16/24 = 12/p
[URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=12&den1=24&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Run this through our proportion calculator[/URL] by typing 16/24 = 12/p into our search engine.
We get [B]p = 18[/B].
A 12 pound roast will feed 18 people.

A 1975 comic book has appreciated 8% per year and originally sold for $0.26. What will the comic boo

A 1975 comic book has appreciated 8% per year and originally sold for $0.26. What will the comic book be worth in 2020
Calculate the number of years:
2020 - 1975 = 45
Set up the accumulation function A(t) where t is the number of years since 1975:
A(t) = 0.26(1.08)^t
We want A(45)
A(45) = 0.26(1.08)^45
A(45) = 0.26 * 32.9045
A(45) = [B]8.30[/B]

a 24 sheet of aluminum is to be cut into 2.5 strips. how wide is the remaining wasted piece of alumi

a 24 sheet of aluminum is to be cut into 2.5 strips. how wide is the remaining wasted piece of aluminum
Divide 24 by 2.5 to get number of sheets:
24/2.5 = 9.6
So we have 9 full sheets. Which means each strip is [B]0.6 wide[/B]

A 3-digit security code can use the numbers 0-9. How many possible combinations are there if the num

A 3-digit security code can use the numbers 0-9. How many possible combinations are there if the numbers can be repeated
[0-9] * [0-9] * [0-9]
10 * 10 * 10 = [B]1,000 combinations[/B]

A 50-pound bowling ball and an 8-pound bowling ball are dropped from a tall building. Which ball wil

A 50-pound bowling ball and an 8-pound bowling ball are dropped from a tall building. Which ball will hit first?
[B]They will land at the same time[/B]
[B]How fast something falls due to gravity is determined by a number known as the "acceleration of gravity", which is 9.81 m/s^2 at the surface of our Earth. In one second, [I]any object[/I]’s downward velocity will increase by 9.81 m/s because of gravity. This is just the way gravity works - it accelerates everything at exactly the same rate.[/B]

A 6-sided die is rolled once. What is the probability of rolling a number less than 4?

A 6-sided die is rolled once. What is the probability of rolling a number less than 4?
Using our [URL='https://www.mathcelebrity.com/1dice.php?gl=4&pl=4&opdice=1&rolist=+2%2C3%2C4&dby=+2%2C3%2C5&montect=+100']one dice calculator[/URL], we get:
P(N < 4) = [B]1/2[/B]

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each pri

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $188,800?
Let x be the number of $24 tickets, and y be the number of $40 tickets. We have:
[LIST=1]
[*]24x + 40y = 188,800
[*]x + y = 6,000
[*]Rearrange (2) to solve for x: x = 6000 - y
[*]Plug in (3) to (1):
[/LIST]
24(6000 - y) + 40y = 188800
144,000 - 24y + 40y = 188,800
16y + 144,000 = 188,800
Subtract 144,000 from each side:
16y = 44,800
Divide each side by 16
y = 2,800 ($40 tickets)
Plug this into (2)
x + 2,800 = 6000
Subtract 2,800 from each side:
x = 3,200 ($24 tickets)

A = himpunan bilangan prima yang kurang dari 20. Banyaknya anggota himpunan A adalah …

A = himpunan bilangan prima yang kurang dari 20. Banyaknya anggota himpunan A adalah …
[URL='https://www.mathcelebrity.com/prime-numbers.php?num=8&pl=Prime+Numbers']Dengan menggunakan kalkulator nombor perdana, kami mendapat[/URL]:
[B]A = {2, 3, 5, 7, 11, 13, 17, 19}[/B]

A bag contains 19 balls numbered 1 through 19. What is the probability that a randomly selected ball

A bag contains 19 balls numbered 1 through 19. What is the probability that a randomly selected ball has an even number?
Even numbers in the bag are {2,4,6,8,10,12,14,16,18}
So we have 9 total even numbers.
Therefore, the probability of drawing an even number is [B]9/19[/B]

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. another m

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. Another marble is taken from the bag. Work out the probability that the two marbles taken from the bag are the same color.
[LIST]
[*]Total number of marbles in the bag is 3 + 4 = 7.
[*]The problem asks for the probability of (RR) [I]or[/I] (BB).
[*]It's worthy to note we are replacing the balls after each draw, which means we always have 7 to draw from
[/LIST]
Since each draw is independent, we take the product of each event for the total event probability.
P(RR) = 3/7 * 3/7 = 9/49
P(BB) = 4/7 * 4/7 = 16/49
We want to know P(RR) + P(BB)
P(RR) + P(BB) = 9/49 + 16/49 = 25/49
[MEDIA=youtube]26F9vjsgNGs[/MEDIA]

A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles. You select one marble at random f

A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles. You select one marble at random from the bag. What is P(blue)
P(blue) = Number of blue marbles / Total Marbles
P(blue) = 5 / (5 + 6 + 4)
P(blue) = 5/15
We can reduce this. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F15&frac2=3%2F8&pl=Simplify']type in 5/15 into our search engine, choose simplify[/URL], and we get:
P(blue) = [B]1/3[/B]

A bag contains 666 red balls, 444 green balls, and 333 blue balls. If we choose a ball, then another

A bag contains 666 red balls, 444 green balls, and 333 blue balls. If we choose a ball, then another ball without putting the first one back in the bag, what is the probability that the first ball will be green and the second will be red?
[U]Calculate total number of balls to start:[/U]
Total Balls = Red Balls + Green Balls + Blue Balls
Total Balls = 666 + 444 + 333
Total Balls = 1,443
[U]Calculate the probability of drawing a green ball on the first pick:[/U]
P(Green) = Green Balls / Total Balls
P(Green) = 444/1443
P(Green) = 0.30769
[U]Calculate the probability of drawing a red ball on the second pick (without replacement):[/U]
Total Balls decrease by 1, since we do not replace. So Total Balls = 1,443 - 1 = 1,442
P(Red) = Red Balls / Total Balls
P(Red) = 666/1442
P(Red) = 0.46186
Now, we want the probability of Green, Red in that order.
Since each event is independent, we multiply the event probabilities
P(Green, Red) = P(Green) * P(Red)
P(Green, Red) = 0.30769 * 0.46186
P(Green, Red) = [B]0.14211[/B]

A bag contains tiles, 3 tiles are red. 6 tiles are green, and 3 tiles are blue. A tile will be rando

A bag contains tiles, 3 tiles are red. 6 tiles are green, and 3 tiles are blue. A tile will be randomly selected from the bag . What is the probability that the tile selected will be green
P(green) = Number of green tiles / Total Tiles
P(green) = 6 / (3 + 6 + 3)
P(green) = 6 / 12
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F12&frac2=3%2F8&pl=Simplify']type in 6/12 into our search engine, pick simplify[/URL], and we get:
P(green) = [B]1/2 or 0.5[/B]

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purch

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 290 feet by 150 feet.
The area of a rectangle is length * width, so we have:
A = 290 * 150
A = 43,500 sq ft.
Now, to find the number of bags needed for a 300 square feet per bag of fertilizer, we have:
Bags Needed = Total Square Feet of Lawn / Square Feet covered per bag
Bags Needed = 43,500 / 300
Bags Needed = [B]145[/B]

A bag of marbles is said to contain 50 marbles to the nearest ten. What is the greatest number of ma

A bag of marbles is said to contain 50 marbles to the nearest ten. What is the greatest number of marbles that could be in the bag and what is the least number of marbles that could be in the bag
The key word in this problem is [I][B]nearest ten[/B][/I].
The nearest ten below 50 starts at 45. Why? Because the last digit is 5. At 5, we round up to the nearest ten.
Therefore, the least number of marbles in the bag is 45 since it rounds up to 50 for the nearest ten
The greatest number above 50 rounded to the nearest ten is 54, because less than 5 on the last digit means we round down.
Therefore, the greatest number of marbles in the bag is 54 since it rounds down to 50 when the last digit is less than 5
Answer:
{[B]45, 54}
[MEDIA=youtube]-cl_OHA8-yc[/MEDIA][/B]

A bag of quarters and nickels is worth $8.30. There are two less than three times as many quarters a

A bag of quarters and nickels is worth $8.30. There are two less than three times as many quarters as nickels. How many of the coins must be quarters?
Assumptions and givens:
[LIST]
[*]Let the number of quarters be q
[*]Let the number of nickels be n
[/LIST]
We have two equations:
[LIST=1]
[*]0.05n + 0.25q = 8.30
[*]n = 3q - 2 [I](Two less than Three times)[/I]
[/LIST]
Plug in equation (2) into equation (1) for q to solve this system of equations:
0.05(3q - 2) + 0.25q = 8.30
To solve this equation for q, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.05%283q-2%29%2B0.25q%3D8.30&pl=Solve']type it in our search engine[/URL] and we get:
q = [B]21[/B]

A baker determined the annual profit in dollars from selling pies using p(n ) = 52n - 0.05n^2, where

A baker determined the annual profit in dollars from selling pies using p(n ) = 52n - 0.05n^2, where n is the number of pies sold. What is the annual profit if the baker sells 700 pies?
p(700) = 52(700) - 0.05(700)^2
p(700) = 36400 - 0.05 * 490000
p(700) = 36400 - 24500
p(700) = [B]11900[/B]

A baker determined the annual profit in dollars from selling pies using p(n) = 52n - 0.05n^2 , where

A baker determined the annual profit in dollars from selling pies using p(n) = 52n - 0.05n^2 , where n is the number of pies sold. What is the annual profit if the baker sells 400 pies?
p(400) = 52(400) - 0.05(400)^2
p(400) = 20800 - 0.05(160000)
p(400) = 20800 - 8000
p(400) = [B]12800[/B]

A bakery has a fixed cost of $119.75 per a day plus $2.25 for each pastry. The bakery would like to

A bakery has a fixed cost of $119.75 per a day plus $2.25 for each pastry. The bakery would like to keep its daily costs at or below $500 per day. Which inequality shows the maximum number of pastries, p, that can be baked each day.
Set up the cost function C(p), where p is the number of pastries:
C(p) = Variable Cost + Fixed Cost
C(p) = 2.25p + 119.75
The problem asks for C(p) at or below $500 per day. The phrase [I]at or below[/I] means less than or equal to (<=).
[B]2.25p + 119.75 <= 500[/B]

A bakery sells 349 pieces pande coco in a day. About how many pande coco bread can bakery shop sell

A bakery sells 349 pieces pande coco in a day. About how many pande coco bread can bakery shop sell in 25 days?
Total pieces of coco = Pieces per day * Number of Days
Total pieces of coco = 349 * 25
Total pieces of coco = [B]8,725[/B]

A bakery sells 5800 muffins in 2010. The bakery sells 7420 muffins in 2015. Write a linear model tha

A bakery sells 5800 muffins in 2010. The bakery sells 7420 muffins in 2015. Write a linear model that represents the number y of muffins that the bakery sells x years after 2010.
Find the number of muffins sold after 2010 through 2015:
7,420 - 5,800 = 1,620
Now, since the problem states a linear sales model, we need to determine the sales per year:
1,620 muffins sold since 2010 / 5 years = 324 muffins per year.
Build our linear model:
[B]y = 5,800 + 324x
[/B]
Reading this out loud, we start with 5,800 muffins at the end of 2010, and we add 324 more muffins for each year after 2010.

A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-f

A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-fourths the height of the previous bounce. Find the total vertical distance travelled by the all in ten bounces.
The height of each number bounce (n) is shown as:
h(n) = 6(0.75)^n
We want to find h(10)
h(n) = 6(0.75)^n
Time Height
0 6
1 4.5
2 3.375
3 2.53125
4 1.8984375
5 1.423828125
6 1.067871094
7 0.8009033203
8 0.6006774902
9 0.4505081177
10 0.3378810883
Adding up each bounce from 1-10, we get:
16.98635674
Since vertical distance means both [B]up and down[/B], we multiply this number by 2 to get:
16.98635674 * 2 = 33.97271347
Then we add in the initial bounce of 6 to get:
33.97271347 + 6 = [B]39.97271347 feet[/B]

A bamboo tree grew 3 inches per day. How many days will it take the tree to grow 144 inches? Choose

A bamboo tree grew 3 inches per day. How many days will it take the tree to grow 144 inches? Choose the correct equation to represent this situation.
Let the number of days be d. We have the equation:
3d = 144
To solve this equation for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=3d%3D144&pl=Solve']type it in our search engine[/URL] and we get:
d = [B]48[/B]

A bank charges a service fee of $7.50 per month for a checking account. A bank account has $85.00. I

A bank charges a service fee of $7.50 per month for a checking account. A bank account has $85.00. If no money is deposited or withdrawn except the service charge, how many months until the account balance is negative?
Let m be the number of months. Our balance is denoted by B(m):
B(m) = 85 - 7.5m
The question asks when B(m) is less than 0. So we set up an inequality:
85 - 7.5m < 0
To solve this inequality for m, [URL='https://www.mathcelebrity.com/1unk.php?num=85-7.5m%3C0&pl=Solve']we type it in our search engine[/URL] and we get:
m > 11.3333
We round up to the next whole integer and get [B]m = 12[/B]

A barn contains cows, ducks, and a 3-legged dog named Tripod. There are twice as many cows as ducks

A barn contains cows, ducks, and a 3-legged dog named Tripod. There are twice as many cows as ducks in the barn and a total of 313 legs. How many ducks are there in the barn?
[LIST]
[*]Let the number of ducks be d. Duck legs = 2 * d = 2d
[*]Number of cows = 2d. Cow legs = 4 * 2d = 8d
[*]1 dog Tripod has 3 legs
[/LIST]
Total legs:
2d + 8d + 3 = 313
Solve for [I]d[/I] in the equation 2d + 8d + 3 = 313
[SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE]
(2 + 8)d = 10d
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
10d + 3 = + 313
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 3 and 313. To do that, we subtract 3 from both sides
10d + 3 - 3 = 313 - 3
[SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE]
10d = 310
[SIZE=5][B]Step 5: Divide each side of the equation by 10[/B][/SIZE]
10d/10 = 310/10
d = [B]31[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=2d%2B8d%2B3%3D313&pl=Solve']Source[/URL]

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a func

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a function to model the situation the value of the card in 2020.Let x be number of years since 1970
The formula for accumulated value of something with a percentage growth p and years x is:
V(x) = Initial Value * (1 + p/100)^x
Set up our growth equation where 8% = 0.08 and V(y) for the value at time x and x = 2020 - 1970 = 50, we have:
V(x) = 100 * (1 + 8/100)^50
V(x) = 100 * (1.08)^50
V(x) = 100 * 46.9016125132
V(x) = [B]4690.16[/B]

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many m

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many more tickets would they need to sell to earn at least $441?
Let the number of tickets above 42 be t.
A few things to note on this question:
[LIST]
[*]The phrase [I]at least[/I] means greater than or equal to, so we have an inequality.
[*]Earnings = Price * Quantity
[/LIST]
We're given:
Earnings = 4.50 * 42 + 4.5t >= 441
Earnings = 189 + 4.5t >= 441
We want to solve this inequality for t:
Solve for [I]t[/I] in the inequality 189 + 4.5t ? 441
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 189 and 441. To do that, we subtract 189 from both sides
4.5t + 189 - 189 ? 441 - 189
[SIZE=5][B]Step 2: Cancel 189 on the left side:[/B][/SIZE]
4.5t ? 252
[SIZE=5][B]Step 3: Divide each side of the inequality by 4.5[/B][/SIZE]
4.5t/4.5 ? 252.4.5
[B]t ? 56[/B]

A baseball player gets 3 hits in the first 15 games of the season. If he continues hitting at the sa

A baseball player gets 3 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games?
We set up a proportion of hits to games where h is the number of hits the player gets in 45 games:
3/15 = h/45
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=h&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']Enter this into our search engine[/URL], and we get [B]h = 9[/B].

A baseball player gets 7 hits in the first 15 games of the season. If he continues hitting at the sa

A baseball player gets 7 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games?
Let's find the proportion of hits to games. Using h as the number of hits in 45 games, we have:
7/15 = h/45
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=7&num2=h&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get h = 21

a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bri

a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bring his average up to 0.400?
Let the amount of consecutive hits needed be h. We have:
hits / at bats = Batting Average
Plugging in our numbers, we get:
(9 + h)/60 = 0.400
Cross multiply:
9 + h = 60 * 0.4
9 + h = 24
To solve this equation for h, [URL='https://www.mathcelebrity.com/1unk.php?num=9%2Bh%3D24&pl=Solve']we type it in our search engine[/URL] and we get:
h = [B]15[/B]

A bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The ave

A bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $80. How many bicycles must the store sell each month to break even?
Profit = Revenue - Cost
Let the number of bikes be b.
Revenue = 80b
Cost = 60b + 1500
Break even is when profit equals 0, which means revenue equals cost. Set them equal to each other:
60b + 1500 = 80b
We [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B1500%3D80b&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]75[/B]

A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The a

A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The average selling price of each bicycle is $95. How many bicycles must the store sell each month to break even?
Let the number of bikes be b.
Set up our cost function, where it costs $45 per bike to produce
C(b) = 45b
Set up our revenue function, where we earn $95 per sale for each bike:
R(b) = 95b
Set up our profit function, which is how much we keep after a sale:
P(b) = R(b) - C(b)
P(b) = 95b - 45b
P(b) = 50b
The problem wants to know how many bikes we need to sell to break-even. Note: break-even means profit equals operating cost, which in this case, is $2,750. So we set our profit function of 50b equal to $2,750
50b = 2750
[URL='https://www.mathcelebrity.com/1unk.php?num=50b%3D2750&pl=Solve']We type this equation into our search engine[/URL], and we get:
b = [B]55[/B]

a bicycle store costs $3600 per month to operate. The store pays an average of $60 per bike. the ave

a bicycle store costs $3600 per month to operate. The store pays an average of $60 per bike. the average selling price of each bicycle is $100. how many bicycles must the store sell each month to break even?
Cost function C(b) where b is the number of bikes:
C(b) = Variable Cost + Fixed Cost
C(b) = Cost per bike * b + operating cost
C(b) = 60b + 3600
Revenue function R(b) where b is the number of bikes:
R(b) = Sale price * b
R(b) = 100b
Break Even is when Cost equals Revenue, so we set C(b) = R(b):
60b + 3600 = 100b
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B3600%3D100b&pl=Solve']type it in our math engine[/URL] and we get:
b = [B]90[/B]

A boat can carry 582 passengers to the base of a waterfall. A total of 13,105 people ride the boat t

A boat can carry 582 passengers to the base of a waterfall. A total of 13,105 people ride the boat today. All the rides are full except for the first ride. How many rides are given?
582 passengers on the boat
Let r be the number of rides
So we want to find r when:
582r = 13105
To solve for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=582r%3D13105&pl=Solve']type this equation into our math engine[/URL] and we get:
r = 22.517
If we round this down, setting 0.517 rides as the first ride, we get:
r = [B]22
[MEDIA=youtube]0J2YRPzKsoU[/MEDIA][/B]

A book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books

A book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books they make sell for $40 each.
[B][U]Set up Cost Function C(b) where b is the number of books:[/U][/B]
C(b) = Fixed Cost + Variable Cost x Number of Units
C(b) = 180,000 + 25(b)
[B]Set up Revenue Function R(b):[/B]
R(b) = 40b
Set them equal to each other
180,000 + 25b = 40b
Subtract 25b from each side:
15b = 180,000
Divide each side by 15
[B]b = 12,000 for break even[/B]

A Bouquet of lillies and tulips has 12 flowers. Lillies cost $3 each, and tulips cost $2 each. The b

A Bouquet of lillies and tulips has 12 flowers. Lillies cost $3 each, and tulips cost $2 each. The bouquet costs $32. Write and solve a system of linear equations to find the number of lillies and tulips in the bouquet.
Let l be the number of lillies and t be the number of tulips. We're given 2 equations:
[LIST=1]
[*]l + t = 12
[*]3l + 2t = 32
[/LIST]
With this system of equations, we can solve it 3 ways.
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[LIST]
[*][B]l = 8[/B]
[*][B]t = 4[/B]
[/LIST]
[B]Now Check Your Work For Equation 1[/B]
l + t = 12
8 + 4 ? 12
12 = 12
[B]Now Check Your Work For Equation 2[/B]
3l + 2t = 32
3(8) + 2(4) ? 32
24 + 8 ? 32
32 = 32

A bowler knocks down at least 6 pins 70 percent of the time. Out of 200 rolls, how many times can yo

A bowler knocks down at least 6 pins 70 percent of the time. Out of 200 rolls, how many times can you predict the bowler will knock down at least 6 pins?
Expected Value of (knocking down at least 6 pins) = number of rolls * probability of knocking down at least 6 pins
Expected Value of (knocking down at least 6 pins) = 200 * 0.7
Expected Value of (knocking down at least 6 pins) = [B]140[/B]

A box of pencils weights 3.25 grams. If the teacher orders 14 boxes, how much would the pencils weig

A box of pencils weights 3.25 grams. If the teacher orders 14 boxes, how much would the pencils weigh?
Total Weight = Number of Boxes * Weight per box
Total Weight = 14 * 3.25
Total Weight = [B]45.5 grams[/B]

A bunny population is doubling every 2 years. There are currently 45 bunnies. How many will there be

A bunny population is doubling every 2 years. There are currently 45 bunnies. How many will there be in 10 years?
Find the number of doubling periods:
Number of Doubling periods = Time / Doubling period
Number of Doubling periods = 10/2
Number of Doubling periods = 5
Create a function to determine the amount of bunnies after each doubling period:
B(n) = 45 * 2^n
Since we calculated 5 doubling periods, we want B(5):
B(5) = 45 * 2^5
B(5) = 45 * 32
B(5) = [B]1,440[/B]

A bus holds 45 students. How many buses were taken on a field trip if 13 students travels by car and

A bus holds 45 students. How many buses were taken on a field trip if 13 students travels by car and total of 320 students went on a trip?
[U]Find the number of students who went on the bus:[/U]
Number of students who went on the bus = Total students on field trip - students who traveled by car
Number of students who went on the bus = 320 - 13
Number of students who went on the bus = 307
Calculate the number of buses needed:
Number of buses needed = Number of students who went on the bus / Bus Capacity
Number of buses needed = 307 / 45
Number of buses needed = 6.822
We round up for a full bus to get [B]7 buses[/B]

A bus ride cost 1.50. A 30 day pass cost $24. Write an inequallity to show that the 30 day pass is t

A bus ride cost 1.50. A 30 day pass cost $24. Write an inequallity to show that the 30 day pass is the better deal
Let the number of days be d. We have the inequality below where we show when the day to day cost is greater than the monthly pass:
1.5d > 24
To solve this inequality for d, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.5d%3E24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]d > 16[/B]

A cab charges $5 for the ride plus $1.25 per mile. How much will a 53 mile trip cost?

A cab charges $5 for the ride plus $1.25 per mile. How much will a 53 mile trip cost?
We set up our cost function C(m) where m is the number of miles:
C(m) = 1.25m + 5
The problem asks for C(53):
C(53) = 1.25(53) + 5
C(53) = 66.25 + 5
C(53) = [B]$71.25[/B]

A cab company charges $5 per cab ride, plus an additional $1 per mile driven , How long is a cab rid

A cab company charges $5 per cab ride, plus an additional $1 per mile driven , How long is a cab ride that costs $13?
Let the number of miles driven be m. Our cost function C(m) is:
C(m) = Cost per mile * m + cab cost
C(m) = 1m + 5
The problem asks for m when C(m) = 13:
1m + 5 = 13
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=1m%2B5%3D13&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]8[/B]

A cab company charges $5 per cab ride, plus an additional $3 per mile driven. How long is a cab ride

A cab company charges $5 per cab ride, plus an additional $3 per mile driven. How long is a cab ride that costs $17?
Let m be the number of miles driven. We setup the cost equation C(m):
C(m) = Cost per mile driven * miles driven + ride cost
C(m) = 3m + 5
The questions asks for m when C(m) is 17:
3m + 5 = 17
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%2B5%3D17&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]4[/B]

A cable company charges $75 for installation plus $20 per month. Another cable company offers free i

A cable company charges $75 for installation plus $20 per month. Another cable company offers free installation but charges $35 per month. For how many months of cable service would the total cost from either company be the same
[U]Set ups the cost function for the first cable company C(m) where m is the number of months:[/U]
C(m) = cost per month * m + installation fee
C(m) = 20m + 75
[U]Set ups the cost function for the second cable company C(m) where m is the number of months:[/U]
C(m) = cost per month * m + installation fee
C(m) = 35m
The problem asks for m when both C(m) functions are equal. So we set both C(m) functions equal and solve for m:
20m + 75 = 35m
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=20m%2B75%3D35m&pl=Solve']type this equation into our search engine[/URL] and we get:
m = [B]5[/B]

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drin

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 8 minutes?
Set up a proportion of gallons of water to time where g is the number of gallons of water in 8 minutes.
15/10 = g/8
[URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=g&den1=10&den2=8&propsign=%3D&pl=Calculate+missing+proportion+value']Run this problem through our proportion calculator[/URL] to get [B]g = 12.[/B]

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drin

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 14 minutes?
Set up a proportion of gallons of water over minutes where g is the number of gallons the camel can drink in 14 minutes:
15/10 = g/14
[URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=g&den1=10&den2=14&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
[B]g = 21[/B]

A candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the can

A candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the candlestick is 13.4 inches tall. Write and solve a linear equation to find the original height of the candle.
Let h equal the number of hours the candlestick burns. We have a candlestick height equation of C.
C = 13.4 + 0.2(8) <-- We need to add back the 8 hours of candlestick burning
C = 13.4 + 1.6
C = [B]15 inches[/B]

A car cost 500 how much does 5 cars cost

A car cost 500 how much does 5 cars cost
Total cost = Number of cars * cost per cars
Total cost = 5 * 500
Total cost = [B]2500[/B]

A car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will t

A car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will the car be worth $7300 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.
Set up the depreciation equation D(t) where t is the number of years in the life of the car:
D(t) = 24,000/(1.3)^t
The problem asks for D(t)<=7300
24,000/(1.3)^t = 7300
Cross multiply:
7300(1.3)^t = 24,000
Divide each side by 7300
1.3^t = 24000/7300
1.3^t = 3.2877
Take the natural log of both sides:
LN(1.3^t) = LN(3.2877)
Using the natural log identities, we have:
t * LN(1.3) = 1.1902
t * 0.2624 = 1.1902
Divide each side by 0.2624
t = 4.5356
[B]Rounding this up, we have t = 5[/B]

A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the re

A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the resale value be after 4 years?
Set up a book value function B(t) where t is the number of years after purchase date. If an asset decreases by 30%, we subtract it from the original 100% of the starting value at time t:
B(t) = 19,000(1-0.3)^t
Simplifying this, we get:
B(t) = 19,000(0.7)^t <-- I[I]f an asset decreases by 30%, it keeps 70% of it's value from the prior period[/I]
The problem asks for B(4):
B(4) = 19,000(0.7)^4
B(4) = 19,000(0.2401)
B(4) = [B]4,561.90[/B]

a car is worth 24000 and it depreciates 3000 a year how long till it costs 9000

a car is worth 24000 and it depreciates 3000 a year how long till it costs 9000
Let y be the number of years. We want to know y when:
24000 - 3000y = 9000
Typing [URL='https://www.mathcelebrity.com/1unk.php?num=24000-3000y%3D9000&pl=Solve']this equation into our search engine[/URL], we get:
y = [B]5[/B]

A car rents $35 per day plus 15 cents per mile driven

A car rents $35 per day plus 15 cents per mile driven
Set up the cost function C(m) where m is the number of miles driven:
C(m) = Cost per mile * m + Daily Fee
[B]C(m) = 0.15m + 35[/B]

A car who’s original value was $25600 decreases in value by $90 per month. How Long will it take bef

A car who’s original value was $25600 decreases in value by $90 per month. How Long will it take before the cars value falls below $15000
Let m be the number of months.We have our Book Value B(m) given by:
B(m) = 25600 - 90m
We want to know when the Book value is less than 15,000. So we have an inequality:
25600 - 90m < 15000
Typing [URL='https://www.mathcelebrity.com/1unk.php?num=25600-90m%3C15000&pl=Solve']this inequality into our search engine and solving for m[/URL], we get:
[B]m > 117.78 or m 118 months[/B]

A car worth $43,000 brand new, depreciates at a rate of $2000 per year. What is the formula that des

A car worth $43,000 brand new, depreciates at a rate of $2000 per year. What is the formula that describes the relationship between the value of the car (C) and the time after it has been purchased (t)?
Let t be the number of years since purchase. Depreciation means the value decreases, so we have:
[B]C = 43000 - 2000t[/B]

a carnival charges $6 admission and $2.50 per ride. You have $50 to spend at the carnival. Which of

a carnival charges $6 admission and $2.50 per ride. You have $50 to spend at the carnival. Which of the following inequalities represents the situation if r is the number of rides?
We set up our inequality using less than or equal to, since our cash is capped at $50. We use S for our :
Cost per ride * r + Admission <= 50
Plugging in our numbers, we get:
2.50r + 6 <= 50
[B][/B]
Now, if the problem asks you to put this in terms of r, then [URL='https://www.mathcelebrity.com/1unk.php?num=2.50r%2B6%3C%3D50&pl=Solve']we plug this inequality into our search engine[/URL] and we get:
r <= 17.6
Since we cannot do fractional rides, we round down to 17:
[B]r <= 17[/B]

A carnival charges a $15 admission price. Each game at the carnival costs $4. How many games would a

A carnival charges a $15 admission price. Each game at the carnival costs $4. How many games would a person have to play to spend at least $40?
Let g be the number of games. The Spend function S(g) is:
S(g) = Cost per game * number of games + admission price
S(g) = 4g + 15
The problem asks for g when S(g) is at least 40. At least is an inequality using the >= sign:
4g + 15 >= 40
To solve this inequality for g, we type it in our search engine and we get:
g >= 6.25
Since you can't play a partial game, we round up and get:
[B]g >= 7[/B]

A car’s purchase price is $24,000. At the end of each year, the value of the car is three-quarters o

A car’s purchase price is $24,000. At the end of each year, the value of the car is three-quarters of the value at the beginning of the year. Write the first four terms of the sequence of the car’s value at the end of each year.
three-quarters means 3/4 or 0.75. So we have the following function P(y) where y is the number of years since purchase price:
P(y) = 24000 * 0.75^y
First four terms:
P(1) = 24000 * 0.75 = [B]18000[/B]
P(2) = 18000 * 0.75 = [B]13500[/B]
P(3) = 13500 * 0.75 = [B]10125[/B]
P(4) = 10125 * 0.75 = [B]7593.75[/B]

A cash register contains $5 bills and $20 bills with a total value of $180 . If there are 15 bills t

A cash register contains $5 bills and $20 bills with a total value of $180 . If there are 15 bills total, then how many of each does the register contain?
Let f be the number of $5 dollar bills and t be the number of $20 bills. We're given the following equations:
[LIST=1]
[*]f + t = 15
[*]5f + 20t = 180
[/LIST]
We can solve this system of equations 3 ways. We get [B]t = 7[/B] and [B]f = 8[/B].
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]

A celebrity 50,000 followers on Instagram. The number of follower increases 45% each year. How many

A celebrity 50,000 followers on Instagram. The number of follower increases 45% each year. How many followers will they have after 8 years?
We set up a growth equation for followers F(y), where y is the number of years passed since now:
F(y) = 50000 * (1.45)^y <-- since 45% is 0.45
The problem asks for F(8):
F(8) = 50000 * 1.45^8
F(8) = 50000 * 19.5408755063
F(8) = [B]977,044[/B]

A cell phone company charges 8$ per minute. How much do you pay for 60 minutes?

A cell phone company charges 8$ per minute. How much do you pay for 60 minutes?
Calculate the total bill:
Total Bill = Cost per minute * number of minutes
Total Bill = $8 * 60
Total Bill = [B]$480[/B]

A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for m mi

A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for m minutes is $21.20. Write an equation that models this situation.
Let m be the number of minutes. We have the cost equation C(m):
[B]0.25m + 12.95 = $21.20[/B]

A cell phone plan charges $1.25 for the first 400 minutes and $0.25 for each additional minute, x. W

A cell phone plan charges $1.25 for the first 400 minutes and $0.25 for each additional minute, x. Which represents the cost of the cell phone plan?
Let C(x) be the cost function where x is the number of minutes we have:
[B]C(x) = 1.25(min(400, x)) + 0.25(Max(0, 400 - x))[/B]

A cell phone plan costs $20 a month and includes 200 free minutes. Each additional minute costs 5 ce

A cell phone plan costs $20 a month and includes 200 free minutes. Each additional minute costs 5 cents. If you use your cell phone for at least 200 minutes a month, write a function C(x) that represents the total cost per x minutes.
We add the flat rate per month to 5% of the number of minutes [U]over[/U] 200:
[B]C(x) = 20 + 0.05(x - 200)[/B]

A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 pe

A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 per month. However, if you go over your 5 GB of data in a month, you have to pay an extra $10 for each GB. How many GB would be used to make both plans cost the same?
Let g be the number of GB.
The limited plan has a cost as follows:
C = 10(g - 5) + 55
C = 10g - 50 + 55
C = 10g + 5
We want to set the limited plan equal to the unlimited plan and solve for g:
10g + 5 = 70
Solve for [I]g[/I] in the equation 10g + 5 = 70
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 5 and 70. To do that, we subtract 5 from both sides
10g + 5 - 5 = 70 - 5
[SIZE=5][B]Step 2: Cancel 5 on the left side:[/B][/SIZE]
10g = 65
[SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE]
10g/10 = 65/10
g = [B]6.5[/B]
Check our work for g = 6.5:
10(6.5) + 5
65 + 5
70

A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 p

A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 people if 3 people initially exposes? Round to the nearest hour.
Let h be the number of hours. We have the equation:
3 * (1.1)^h = 1,200
Divide each side by 3:
1.1^h = 400
[URL='https://www.mathcelebrity.com/natlog.php?num=1.1%5Eh%3D400&pl=Calculate']Type this equation into our search engine [/URL]to solve for h:
h = 62.86
To the nearest hour, we round up and get [B]h = 63[/B]

A certain number added to its square is 30

Let x be the number. We have:
x^2 + x = 30
Subtract 30 from each side:
x^2 + x - 30 = 0
Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-30%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get potential solutions of:
[B]x = 5 or x = -6[/B]
Check 5:
5 + 5^2 = 5 + 25 = [B]30[/B]
Check -6
-6 + -6^2 = -6 + 36 = [B]30[/B]

A certain species of fish costs $3.19 each. You can spend at most $35. How many of this type of f

A certain species of fish costs $3.19 each. You can spend at most $35. How many of this type of fish can you buy for your aquarium?
Let the number of fish be f. We have the following inequality where "at most" means less than or equal to:
3.19f <= 35
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3.19f%3C%3D35&pl=Show+Interval+Notation']Typing this inequality into our search engine[/URL], we get:
f <= 10.917
Since we need a whole number of fish, we can buy a maximum of [B]10 fish[/B].

A checking account is set up with an initial balance of $2400 and $200 are removed from the account

A checking account is set up with an initial balance of $2400 and $200 are removed from the account each month for rent right and equation who solution is the number of months and it takes for the account balance to reach 1000
200 is removed, so we subtract. Let m be the number of months. We want the following equation:
[B]2400 - 200m = 1000
[/B]
Now, we want to solve this equation for m. So [URL='https://www.mathcelebrity.com/1unk.php?num=2400-200m%3D1000&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]7[/B]

A chest of treasure was hidden in the year 64 BC and found in 284 AD. For how long was the chest hid

A chest of treasure was hidden in the year 64 BC and found in 284 AD. For how long was the chest hidden
BC stands for Before Christ. Year 0 is when Christ was born. AD stands for After Death
On a number line, the point of Christ's birth is 0.
So BC is really negative
AD is positive
So we have:
284 - -64
284 + 64
[B]348 years[/B]

A city doubles its size every 48 years. If the population is currently 400,000, what will the popula

A city doubles its size every 48 years. If the population is currently 400,000, what will the population be in 144 years?
Calculate the doubling time periods:
Doubling Time Periods = Total Time / Doubling Time
Doubling Time Periods = 144/48
Doubling Time Periods = 3
Calculate the city population where t is the doubling time periods:
City Population = Initital Population * 2^t
Plugging in our numbers, we get:
City Population = 400,000 * 2^3
City Population = 400,000 * 8
City Population = [B]3,200,000[/B]

A city has a population of 240,000 people. Suppose that each year the population grows by 7.25%. Wha

A city has a population of 240,000 people. Suppose that each year the population grows by 7.25%. What will the population be after 9 years?
Let's build a population function P(t), where t is the number of years since right now.
P(t) = 240,000(1.0725)^t <-- 7.25% as a decimal is 0.0725
The question asks for P(9)
P(9) = 240,000(1.0725)^9
P(9) = 240,000(1.87748)
P(9) = [B]450,596[/B]

A city has a population of 260,000 people. Suppose that each year the population grows by 8.75% . W

A city has a population of 260,000 people. Suppose that each year the population grows by 8.75% . What will the population be after 12 years? Use the calculator provided and round your answer to the nearest whole number.
Using our [URL='http://www.mathcelebrity.com/population-growth-calculator.php?num=acityhasapopulationof260000people.supposethateachyearthepopulationgrowsby8.75%.whatwillthepopulationbeafter12years?usethecalculatorprovidedandroundyouranswertothenearestwholenumber&pl=Calculate']population growth calculator,[/URL] we get P = [B]711,417[/B]

A class has 35 boys and girls. There are 7 more girls than boys. Find the number of girls and boys i

A class has 35 boys and girls. There are 7 more girls than boys. Find the number of girls and boys in the class
Let the number of boys be b and the number of girls be g. We're given two equations:
[LIST=1]
[*]b + g = 35
[*]g = b + 7 (7 more girls means we add 7 to the boys)
[/LIST]
To solve for b, we substitute equation (2) into equation (1) for g:
b + b + 7 = 35
To solve for b, we type this equation into our search engine and we get:
b = [B]14[/B]
Now, to solve for g, we plug b = 14 into equation (2) above:
g = 14 + 7
g = [B]21[/B]

A classroom fish tank contains x goldfish. The tank contains 4 times as many guppies as goldfish. En

A classroom fish tank contains x goldfish. The tank contains 4 times as many guppies as goldfish. Enter an equation that represents the total number of guppies, y, in the fish tank.
The phrase [I]4 times as many[/I] means we multiply the goldfish (x) by 4 to get the number of guppies (y):
[B]y = 4x[/B]

A coin is tossed and a die is rolled. Find the probability pf getting a head and a number greater th

A coin is tossed and a die is rolled. Find the probability pf getting a head and a number greater than 4.
Since each event is independent, we multiply the probabilities of each event.
P(H) = 0.5 or 1/2
P(Dice > 4) = P(5) + P(6) = 1/6 + 1/6 = 2/6 = 1/3
P(H) AND P(Dice > 4) = 1/2 * 1/3 = [B]1/6[/B]

a collection of 7 pencils, every week 3 more pencils are added How many weeks will it take to have 3

a collection of 7 pencils, every week 3 more pencils are added How many weeks will it take to have 30 pencils?
Set up a function, P(w), where w is the number of weeks, and P(w) is the total amount of pencils after w weeks. We have:
P(w) = 3w + 7
We want to know what w is when P(w) = 30
3w + 7 = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=3w%2B7%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get:
w = 7.6667
We round up to the nearest integer, so we get [B]w = 8[/B]

A collection of nickels and dime has a total value of $8.50. How many coins are there if there are 3

A collection of nickels and dime has a total value of $8.50. How many coins are there if there are 3 times as many nickels as dimes.
Let n be the number of nickels. Let d be the number of dimes. We're give two equations:
[LIST=1]
[*]n = 3d
[*]0.1d + 0.05n = 8.50
[/LIST]
Plug equation (1) into equation (2) for n:
0.1d + 0.05(3d) = 8.50
Multiply through:
0.1d + 0.15d = 8.50
[URL='https://www.mathcelebrity.com/1unk.php?num=0.1d%2B0.15d%3D8.50&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]d = 34[/B]
Now, we take d = 34, and plug it back into equation (1) to solve for n:
n = 3(34)
[B]n = 102[/B]

A colony of 995 bacteria doubles in size every 206 minutes. What will the population be 618 minutes

A colony of 995 bacteria doubles in size every 206 minutes. What will the population be 618 minutes from now?
Calculate the doubling time periods:
Doubling Time Periods = Total Minutes From Now / Doubling Period in Minutes
Doubling Time Periods = 618/206
Doubling Time Periods = 3
Calculate the new population using the doubling time formula below where t is the number of doubling periods:
Population = Initial Population * 2^2
Population = 995 * 2^3
Population = 995 * 8
Population = [B]7,960[/B]

A company charges $7 for a T-Shirt and ships and order for $22. A school principal ordered a number

A company charges $7 for a T-Shirt and ships and order for $22. A school principal ordered a number of T-shirts for the school store. The total cost of the order was $1,520. Which equation can be used to find the number one f shirts ordered?
Set up the cost equation C(f) where f is the number of shirts:
C(f) = Cost per shirt * f + Shipping
We're given C(f) = 1520, Shipping = 22, and cost per shirt is 7, so we have:
[B]7f + 22 = 1520
[/B]
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=7f%2B22%3D1520&pl=Solve']type this equation in our search engine[/URL] and we get:
f = [B]214[/B]

A company had sales of $19,808 million in 1999 and $28,858 million in 2007. Use the Midpoint Formula

A company had sales of $19,808 million in 1999 and $28,858 million in 2007. Use the Midpoint Formula to estimate the sales in 2003
2003 is the midpoint of 1999 and 2007, so we use our [URL='https://www.mathcelebrity.com/mptnline.php?ept1=19808&empt=&ept2=28858&pl=Calculate+missing+Number+Line+item']midpoint calculator[/URL] to get:
[B]24,333[/B] sales in 2003

A company has 3,100 employees and is expected to grow at a rate of 0.04 for the next six years. How

A company has 3,100 employees and is expected to grow at a rate of 0.04 for the next six years. How many employees will they have in 6 years? Round to the nearest whole number.
We build the following exponential equation:
Final Balance = Initial Balance * (1 + growth rate)^time
Final Balance = 3100(1.04)^6
Final Balance = 3100 * 1.2653190185
Final Balance = 3922.48895734
The problem asks us to round to the nearest whole number. Since 0.488 is less than 0.5, we round [U]down.[/U]
Final Balance = [B]3,922[/B]

A company has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item tha

A company has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item that it makes has its own cost of $34. One month the company filled an order for 2400 of its tapestries, selling each item for $63. How much profit was generated by the order?
[U]Set up Cost function C(t) where t is the number of tapestries:[/U]
C(t) = Cost per tapestry * number of tapestries + Fixed Cost
C(t) = 34t + 26000
[U]Set up Revenue function R(t) where t is the number of tapestries:[/U]
R(t) = Sale Price * number of tapestries
R(t) = 63t
[U]Set up Profit function P(t) where t is the number of tapestries:[/U]
P(t) = R(t) - C(t)
P(t) = 63t - (34t + 26000)
P(t) = 63t - 34t - 26000
P(t) = 29t - 26000
[U]The problem asks for profit when t = 2400:[/U]
P(2400) = 29(2400) - 26000
P(2400) = 69,600 - 26,000
P(2400) = [B]43,600[/B]

A company has a fixed cost of $34,000 and a production cost of $6 for each unit it manufactures. A u

A company has a fixed cost of $34,000 and a production cost of $6 for each unit it manufactures. A unit sells for $15
Set up the cost function C(u) where u is the number of units is:
C(u) = Cost per unit * u + Fixed Cost
C(u) = [B]6u + 34000[/B]
Set up the revenue function R(u) where u is the number of units is:
R(u) = Sale price per unit * u
R(u) = [B]15u[/B]

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 100x dollars, w

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 + 100x dollars, where x is the number of units produced and sold. How many units will give a profit
Profit P(x) is given by:
R(x) - C(x)
So we have:
P(x) = 500x - (100x + 48,000)
P(x) = 500x - 100x - 48,000
P(x) = 400x - 48,000
A profit is found when P(x) > 0, so we have:
400x - 48000 > 0
To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=400x-48000%3E0&pl=Solve']we type it into our search engine [/URL]and we get:
[B]x > 120[/B]

A company makes a puzzle that is made of 53 small plastic cubes. The puzzles are shipped in boxes th

A company makes a puzzle that is made of 53 small plastic cubes. The puzzles are shipped in boxes that each contain 52 puzzles. That boxes are loaded into trucks that each contain 53 boxes. What is the total number of small plastic cubes in each truck?
1 truck has 53 boxes, and each box contains 52 puzzles, and each puzzle has 53 small plastic cubes.
We have 53 * 52 * 53 = [B]146,068 plastic cubes[/B]

A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat.

A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat. They sell boats for $75 a piece. How many boats must be sold each month to break even?
[U]Set up Cost function C(b) where t is the number of tapestries:[/U]
C(b) = Cost per boat * number of boats + Fixed Cost
C(b) = 50b + 1500
[U]Set up Revenue function R(b) where t is the number of tapestries:[/U]
R(b) = Sale Price * number of boats
R(b) = 75b
[U]Break even is where Revenue equals Cost, or Revenue minus Cost is 0, so we have:[/U]
R(b) - C(b) = 0
75b - (50b + 1500) = 0
75b - 50b - 1500 = 0
25b - 1500 = 0
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-1500%3D0&pl=Solve']type this equation in our math engine[/URL] and we get:
b = [B]60[/B]

A company now has 4900 employees nationwide. It wishes to reduce the number of employees by 300 per

A company now has 4900 employees nationwide. It wishes to reduce the number of employees by 300 per year through retirements, until its total employment is 2560. How long will this take?
Figure out how many reductions are needed
4900 - 2560 = 2340
We want 300 per year for retirements, so let x equal how many years we need to get 2340 reductions.
300x = 2340
Divide each side by 300
x = 7.8 years.
If we want full years, we would do 8 full years

A company specializes in personalized team uniforms. It costs the company $15 to make each uniform a

A company specializes in personalized team uniforms. It costs the company $15 to make each uniform along with their fixed costs at $640. The company plans to sell each uniform for $55.
[U]The cost function for "u" uniforms C(u) is given by:[/U]
C(u) = Cost per uniform * u + Fixed Costs
[B]C(u) = 15u + 640[/B]
Build the revenue function R(u) where u is the number of uniforms:
R(u) = Sale Price per uniform * u
[B]R(u) = 55u[/B]
Calculate break even function:
Break even is where Revenue equals cost
C(u) = R(u)
15u + 640 = 55u
To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=15u%2B640%3D55u&pl=Solve']type this equation into our search engine[/URL] and we get:
u = [B]16
So we break even selling 16 uniforms[/B]

A companys cost function is C(x) = 16x2 + 900 dollars, where x is the number of units. Find th

A companys cost function is C(x) = 16x^2 + 900 dollars, where x is the number of units. Find the marginal cost function.
Marginal Cost is the derivative of the Cost function.
[B]C'(x) = 32x[/B]

A company’s number of personnel on active duty (not on sick leave or vacation leave) during the peri

A company’s number of personnel on active duty (not on sick leave or vacation leave) during the period 2000 - 2013 can be approximated by the cubic model f(x) = 2.5x^3 - 15x^2 - 80x + 1025, where x = 0 corresponds to 2000. Based on the model, how many personnel were on active duty in 2010? What is the domain of f?
If x = 0 corresponds to 2000, when 2010 is 2010 - 2000 = 10. We want f(10):
f(10) = 2.5(10)^3 - 15(10)^2 - 80(10) + 1025
f(10) = 2.5(1000) - 15(100) - 800 + 1025
f(10) = 2500 - 1500 - 800 + 1025
f(10) = [B]1,225[/B]

A computer randomly generates a whole number from 1 to 25. Find the probability that the computer ge

A computer randomly generates a whole number from 1 to 25. Find the probability that the computer generates a multiple of 5
[URL='https://www.mathcelebrity.com/factoriz.php?num=25&pl=Show+Factorization']Multiples of 5[/URL]:
{1, 5, 25}
So we have the probability of a random number multiple of 5 is
[B]3/25[/B]

A construction company can remove 2/3 tons of dirt from a construction site each hour. How long wil

A construction company can remove 2/3 tons of dirt from a construction site each hour. How long will it take them to remove 30 tons of dirt from the site?
Let h be the number of hours. We have the following equation:
2/3h = 30
Multiply each side by 3:
2(3)h/3 = 30 * 3
Cancel the 3 on the left side:
2h = 90
[URL='https://www.mathcelebrity.com/1unk.php?num=2h%3D90&pl=Solve']Type 2h = 90 into the search engine[/URL], we get [B]h = 45[/B].

A construction company needs to remove 24 tons of dirt from a construction site. They can remove 3/8

A construction company needs to remove 24 tons of dirt from a construction site. They can remove 3/8 ton s of dirt each hour. How long will I it take to remove the dirt?
Let h be the number of hours it takes, we have:
3/8h = 24
Multiply each side by 8/3
h = 24(8)/3
24/3 = 8, so we have:
h = 8(8)
h = [B]64 hours[/B]

A contractor’s crew can frame 3 houses in a week. How long will it take them to frame 54 houses if t

A contractor’s crew can frame 3 houses in a week. How long will it take them to frame 54 houses if they frame the same number each week?
54 houses / 3 houses per week = [B]18 weeks[/B]

A cook has 2 3/4 pounds of ground beef. How many quarter-pound burgers can he make?

A cook has 2 3/4 pounds of ground beef. How many quarter-pound burgers can he make?
Using [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%263%2F4&frac2=3%2F8&pl=Simplify']our mixed number calculator[/URL], we see:
2&3/4 = 11/4
A quarter pounder is 1/4, so we have:
11 * (1/4) = 11/4
So we can make [B]11 [/B]quarter pound burgers

A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8

A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8 1/4 cups, how much flour and how much sugar would it be?
Let f be the number of cups of sugar. And let f be the number of cups of flour. We're given two equations:
[LIST=1]
[*]f = 10s
[*]s + f = 8 & 1/4
[/LIST]
Substitute (1) into (2):
s + 10s = 8 & 1/4
11fs= 33/4 <-- 8 & 1/4 = 33/4
Cross multiply:
44s = 33
Divide each side by 44:
s= 33/44
Divide top and bottom by 11 and we get s [B]= 3/4 or 0.75[/B]
Now substitute this into (1):
f = 10(33/44)
[B]f = 330/44 or 7 & 22/44 or 7.5[/B]

A copy machine makes 28 copies per minute. how many copies does it make in 3 minutes and 45 seconds

A copy machine makes 28 copies per minute. how many copies does it make in 3 minutes and 45 seconds?
45 seconds = 45/60 = 3/4 of a minute.
3/4 = 0.75
So we have 3.75 minutes.
Set up a proportion of copies to minutes where c is the number of copies made in 3 minutes and 45 seconds:
28/1 = c/3.75
[URL='https://www.mathcelebrity.com/prop.php?num1=28&num2=c&den1=1&den2=3.75&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our calculator[/URL], we get:
c = [B]105[/B]

A copy machine makes 44 copies per minute. How many copies does it make in 5 minutes and 45 seconds

A copy machine makes 44 copies per minute. How many copies does it make in 5 minutes and 45 seconds
Set up a proportion of copies to minutes where c is the number of copies for 5 minutes and 45 seconds.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=45%2F60&frac2=3%2F8&pl=Simplify']Since 45 seconds[/URL] is:
45/60 = 3/4 of a minute, we have:
5 minutes and 45 seconds = 5.75 minutes
44/1 = c/5.75
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=44&num2=c&den1=1&den2=5.75&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
c = [B]253[/B]

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixe

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixed costs are $110,000 per month and the feed sells for $132 per ton, how many tons should be sold each month to have a monthly profit of $560,000?
[U]Set up the cost function C(t) where t is the number of tons of cattle feed:[/U]
C(t) = Variable Cost * t + Fixed Costs
C(t) = 84t + 110000
[U]Set up the revenue function R(t) where t is the number of tons of cattle feed:[/U]
R(t) = Sale Price * t
R(t) = 132t
[U]Set up the profit function P(t) where t is the number of tons of cattle feed:[/U]
P(t) = R(t) - C(t)
P(t) = 132t - (84t + 110000)
P(t) = 132t - 84t - 110000
P(t) = 48t - 110000
[U]The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:[/U]
48t - 110000 = 560000
[U]To solve for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=48t-110000%3D560000&pl=Solve']type this equation into our search engine[/URL] and we get:[/U]
t =[B] 13,958.33
If the problem asks for whole numbers, we round up one ton to get 13,959[/B]

A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The tot

A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The total value of the items is $825. How many coins are there?
Let c be the number of coins, and s be the number of stamps. We're given:
[LIST=1]
[*]c + s = 300
[*]3c + 1.5s = 825
[/LIST]
We have a set of simultaneous equations, or a system of equations. We can solve this 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]
No matter which way we pick, we get:
s = 50
c = [B]250[/B]

A culture of bacteria doubles every hour. If there are 500 bacteria at the beginning, how many bacte

A culture of bacteria doubles every hour. If there are 500 bacteria at the beginning, how many bacteria will there be after 9 hours?
Assumptions and givens;
[LIST]
[*]h is the number of hours.
[*]B(h) is the number of bacteria at time h
[*]B(0) is the starting bacteria amount
[*]Doubling means multiplying by 2, so we have:
[/LIST]
B(h) = B(0) * 2^h
We want h = 9, so we have:
B(9) = 500 * 2^9
B(9) = 500 * 512
B(9) = [B]256,000[/B]

A cup of coffee costs $1.75. A monthly unlimited coffee card costs $25.00. Which inequality represe

A cup of coffee costs $1.75. A monthly unlimited coffee card costs $25.00. Which inequality represents the number x of cups of coffee you must purchase for the monthly card to be a better deal?
Let c be the number of cups. We want to know how many cups (x) where:
1.75x > 25
Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.75x%3E25&pl=Show+Interval+Notation']inequality solver[/URL], we see:
[B]x > 14.28[/B]

A daily pass costs $62. A season ski pass costs $450. The skier would have to rent skis with eithe

A daily pass costs $62. A season ski pass costs $450. The skier would have to rent skis with either pass for $30 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Let d be the number of days the skier attends.
Calculate the daily cost:
Daily Total Cost = Daily Cost + Rental Cost
Daily Total Cost = 62d + 30d
Daily Total Cost = 92d
Calculate Season Cost:
Season Total Cost = Season Fee + Rental Cost
Season Total Cost = 450 + 30d
Set the daily total cost and season cost equal to each other:
450 + 30d = 92d
[URL='https://www.mathcelebrity.com/1unk.php?num=450%2B30d%3D92d&pl=Solve']Typing this equation into the search engine[/URL], we get d = 7.258.
We round up to the next full day of [B]8[/B].
Now check our work:
Daily Total Cost for 8 days = 92(8) = 736
Season Cost for 8 days = 30(8) + 450 = 240 + 450 = 710.
Therefore, the skier needs to go at least [B]8 days[/B] to make the season cost less than the daily cot.

A department store buys 100 shirts at a cost of $600 and sells them at a selling price of 10 each fi

A department store buys 100 shirts at a cost of $600 and sells them at a selling price of 10 each find the percentage mark up
Find Unit Cost:
Unit Cost = Cost / Number of Shirts
Unit Cost = 600 / 100
Unit Cost = 6
With a selling price of 10, our markup percentage is:
Markup % = 100 * (New Price - Old Price)/Old Price
Markup % = 100 * (10 - 6)/6
Markup % = 100 * 4/6
Markup % = 400/6
Markup % = [B]66.67%[/B]

A dish company needs to ship an order of 893 glass bowls. If each shipping box can hold 19 bowls, ho

A dish company needs to ship an order of 893 glass bowls. If each shipping box can hold 19 bowls, how many boxes will the company need?
Number of boxes needed = Total bowls / Glass bowls per box
Number of boxes needed = 893/19
Number of boxes needed = [B]47[/B]

A diving board is 10 feet long and 1 foot wide. What is its area?

A diving board is 10 feet long and 1 foot wide. What is its area?
A diving board is a rectangle. And the area of a rectangle is:
A = lw
Plugging in our numbers, we get:
A = 10(1)
A = [B]10 sq feet[/B]

A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog wa

A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog walker charge for a 3 hour walk?
Set up the cost equation C(h) where h is the number of hours:
C(h) = Hourly rate * h + flat rate
C(h) = 30h + 6
The question asks for C(h) when h = 3:
C(3) = 30(3) + 6
C(3) = 90 + 6
C(3) = [B]96[/B]

A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with

A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket that costs $19 per ticket. The Web site charges a fee of $16 for the entire purchase. The family is charged a total of $1132. How many tickets did the family buy?
Let t be the number of tickets. We have the following equation with ticket price, insurance, and flat fee:
167t + 19t + 16 = 1132
Combine like terms:
186t + 16 = 1132
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=186t%2B16%3D1132&pl=Solve']equation calculator[/URL], we have:
[B]t = 6[/B]

A family decides to rent a canoe for an entire day. The canoe rental rate is $50 for the first three

A family decides to rent a canoe for an entire day. The canoe rental rate is $50 for the first three hours and then 20$ for each additional hour. Suppose the family can spend $110 for the canoe rental. What is the maximum number of hours the family can rent the canoe?
IF we subtract the $50 for the first 3 hours, we get:
110 - 50 = 60 remaining
Each additional hour is 20, so the max number of hours we can rent the canoe is
$60/20 = 3 hours additional plus the original 3 hours is [B]6 hours[/B]

a family went to a baseball game. the cost to park the car was $5 AND THE COST PER TICKET WAS $21. W

a family went to a baseball game. the cost to park the car was $5 AND THE COST PER TICKET WAS $21. WRITE A LINEAR FUNCTION IN THE FORM Y=MX+B, FOR THE TOTAL COST OF GOING TO THE BASEBALL GAME,Y, AND THE TOTAL NUMBER PEOPLE IN THE FAMILY,X.
We have:
[B]y = 21x + 5[/B]
Since the cost of each ticket is $21, we multiply this by x, the total number of people in the family.
We add 5 as the cost to park the car, which fits the entire family, and is a one time cost.

A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at

A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at a profit of 4 per pig. His total profit was $56. How many pigs did he originally buy?
Let p be the purchase price of pigs. We're given:
[LIST]
[*]Farmer originally bought [I]p [/I]pigs for 232 which is our cost C.
[*]5 of them died, so he has p - 5 left
[*]He sells 4(p - 5) pigs for a revenue amount R
[*]Since profit is Revenue - Cost, which equals 56, we have:
[/LIST]
Calculate Profit
P = R - C
Plug in our numbers:
4(p - 5) - 232 = 56
4p - 20 - 232 = 56
To solve for p, [URL='https://www.mathcelebrity.com/1unk.php?num=4p-20-232%3D56&pl=Solve']we type this equation into our search engine[/URL] and we get:
p = [B]77[/B]

A farmer has a total of 200 ducks and cows in his barn. If he has n cows, how many total legs are th

A farmer has a total of 200 ducks and cows in his barn. If he has n cows, how many total legs are there in the barn? (Make sure you include the farmer.)
[LIST]
[*]Number of cows = n
[*]Legs per cow = 4
[*]Cows legs = 4n
[*]Number of ducks = 200 - n
[*]Legs per duck = 2
[*]Number of ducks legs = (200 - n) x 2 = 400 - 2n
[*]Farmers legs = 2
[/LIST]
Total legs = Cows legs + Ducks Legs + Farmers Legs
Total legs = 4n + 400 - 2n + 2
Total legs = [B]2n + 402[/B]

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over all

A farmer is taking her eggs to the market in a cart, but she hits a
pothole, which knocks over all the containers of eggs. Though she is
unhurt, every egg is broken. So she goes to her insurance agent, who
asks her how many eggs she had. She says she doesn't know, but she
remembers somethings from various ways she tried packing the eggs.
When she put the eggs in groups of two, three, four, five, and six
there was one egg left over, but when she put them in groups of seven
they ended up in complete groups with no eggs left over.
What can the farmer figure from this information about the number of
eggs she had? Is there more than one answer?
We need a number (n) that leaves a remainder of 1 when divided by 2, 3, 4, 5, 6 but no remainder when divided by 7.
217 + 84 = [B]301[/B].
Other solutions are multiples of 3 x 4 x 5 x 7, but we want the lowest one here.

A Farmer Sell products at the market in 38- pound crates. If he sells 100 crates . How many pounds o

A Farmer Sell products at the market in 38- pound crates. If he sells 100 crates . How many pounds of produce has he sold
[U]Calculate the pounds of produce:[/U]
Pounds of Produce = Number of Crates * pounds per crate
Pounds of Produce = 100 crates * 38 pounds per crates
Pounds of Produce = [B]3,800 pounds of produce[/B]3

A farmer was 1/3 of his land to grow corn, a quarter of his land to grow lettuce, and 12.5% of his l

A farmer was 1/3 of his land to grow corn, a quarter of his land to grow lettuce, and 12.5% of his land to grow green beans. He uses the remaining 7 acres to grow wheat.How many total acres does the farmer own?
Convert all land portions to fractions or decimals. We will do fractions:
[LIST]
[*]1/3 for corn
[*][I]A quarter[/I] means 1/4 for lettuce
[*]12.5% is 12.5/100 or 1/8 for green beans
[/LIST]
Now add all these up:
1/3 + 1/4 + 1/8
We need a common factor for 3, 4, and 8. Using our [URL='https://www.mathcelebrity.com/gcflcm.php?num1=3&num2=4&num3=8&pl=LCM']LCM Calculator[/URL], we get 24.
1/3 = 8/24
1/4 = 6/24
18 = 3/24
Add them all up:
(8 + 6 + 3)/24
17/24
This means 17/24 of the land is used for everything but wheat. Wheat occupies (24-17)/24 = 7/24 of the land.
We'll use a for the number of acres on the farm.
7a/24 = 7
[B]a = 24[/B]

A first number plus twice a second number is 10. Twice the first number plus the second totals 29. F

A first number plus twice a second number is 10. Twice the first number plus the second totals 29. Find the numbers.
Let the first number be x. Let the second number be y. We are given the following two equations:
[LIST=1]
[*]x + 2y = 10
[*]2x + y = 29
[/LIST]
We can solve this 3 ways using:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Substitution']Substitution[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Elimination']Elimination[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
Using any of the 3 methods, we get the same answers of [B](x, y) = (16, -3)[/B]

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. F

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. Find the numbers.
[U]The phrase [I]a number[/I] means an arbitrary variable[/U]
A first number is written as x
A second number is written as y
[U]Twice a second number means we multiply y by 2:[/U]
2y
[U]A first number plus twice a second number:[/U]
x + 2y
[U]A first number plus twice a second number is 10 means we set x + 2y equal to 10:[/U]
x + 2y = 10
[U]Twice the first number means we multiply x by 2:[/U]
2x
[U]Twice the first number plus the second:[/U]
2x + y
[U]Twice the first number plus the second totals 35 means we set 2x + y equal to 35:[/U]
2x + y = 35
Therefore, we have a system of two equations:
[LIST=1]
[*]x + 2y = 10
[*]2x + y = 35
[/LIST]
Since we have an easy multiple of 2 for the x variable, we can solve this by multiply the first equation by -2:
[LIST=1]
[*]-2x - 4y = -20
[*]2x + y = 35
[/LIST]
Because the x variables are opposites, we can add both equations together:
(-2 + 2)x + (-4 + 1)y = -20 + 35
The x terms cancel, so we have:
-3y = 15
To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D15&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]-5
[/B]
Now we substitute this y = -5 into equation 2:
2x - 5 = 35
To solve this equation for x, we[URL='https://www.mathcelebrity.com/1unk.php?num=2x-5%3D35&pl=Solve'] type it in our search engine[/URL] and we get:
x = [B]20[/B]

A first number plus twice a second number is 11. Twice the first number plus the second totals 34. F

A first number plus twice a second number is 11. Twice the first number plus the second totals 34. Find the numbers.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x + 2y = 11
[*]2x + y = 34
[/LIST]
Using our simultaneous equations calculator, we have 3 methods to solve this:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
All 3 methods give the same solution:
[LIST]
[*][B]x = 19[/B]
[*][B]y = -4[/B]
[/LIST]

A first number plus twice a second number is 14. Twice the first number plus the second totals 40. F

A first number plus twice a second number is 14. Twice the first number plus the second totals 40. Find the numbers.
[B][U]Givens and assumptions:[/U][/B]
[LIST]
[*]Let the first number be x.
[*]Let the second number be y.
[*]Twice means multiply by 2
[*]The phrases [I]is[/I] and [I]totals[/I] mean equal to
[/LIST]
We're given two equations:
[LIST=1]
[*]x + 2y = 14
[*]2x + y = 40
[/LIST]
To solve this system, we can take a shortcut, and multiply the top equation by -2 to get our new system:
[LIST=1]
[*]-2x - 4y = -28
[*]2x + y = 40
[/LIST]
Now add both equations together
(-2 _ 2)x (-4 + 1)y = -28 + 40
-3y = 12
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D12&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]-4
[/B]
We substitute this back into equation 1 for y = -4:
x + 2(-4) = 14
x - 8 = 14
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-8%3D14&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]22[/B]

A first number plus twice a second number is 22. Twice the first number plus the second totals 28. F

A first number plus twice a second number is 22. Twice the first number plus the second totals 28. Find the numbers.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x + 2y = 22 <-- Since twice means multiply by 2
[*]2x + y = 28 <-- Since twice means multiply by 2
[/LIST]
We have a set of simultaneous equations. We can solve this three ways
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28+&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*][B]x = 11 & 1/3[/B]
[*][B]y = 5 & 1/3[/B]
[/LIST]

A first number plus twice a second number is 3. Twice the first number plus the second totals 24.

A first number plus twice a second number is 3. Twice the first number plus the second totals 24.
Let the first number be x. Let the second number be y. We're given:
[LIST=1]
[*]x + 2y = 3 <-- Because [I]twice[/I] means multiply by 2
[*]2x + y = 24 <-- Because [I]twice[/I] means multiply by 2
[/LIST]
We have a system of equations. We can solve it any one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which way we choose, we get:
[LIST]
[*]x = [B]15[/B]
[*]y = [B]-6[/B]
[/LIST]

A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Fi

A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Find the numbers.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x + 2y = 6
[*]2x + y = 15
[/LIST]
Multiply the first equation by -2:
[LIST=1]
[*]-2x - 4y = -12
[*]2x + y = 15
[/LIST]
Now add them
-2x + 2x - 4y + y = -12 + 15
-3y = 3
Divide each side by -3:
y = 3/-3
y =[B] -1[/B]
Plug this back into equation 1:
x + 2(-1) = 6
x - 2 = 6
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-2%3D6&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]8[/B]

A first number plus twice a second number is 7

A first number plus twice a second number is 7
Let the first number be x. Let the second number be y. We're given:
[LIST]
[*]A first number is x
[*]A second number is y
[*]Twice the second number means we multiply y by 2: 2y
[*][I]Plus [/I]means we add x to 2y: x + 2y
[*]The phrase [I]is[/I] means an equation, so we set x + 2y equal to 7
[/LIST]
[B]x + 2y = 7[/B]

A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Fi

A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Find the numbers
Let the first number be a and the second number be b. We have:
[LIST=1]
[*]a + 2b = 7
[*]2a + b = 23
[/LIST]
Rearrange (1) into (3)
(3) a = 7 - 2b
Substitute (3) into (2):
2(7 - 2b) + b = 23
Multiply through:
14 - 4b + b = 23
Combine like terms:
14 - 3b = 23
Subtract 14 from each side:
-3b = 9
Divide each side by -3
[B]b = -3[/B]
Substitute this into (3)
a = 7 - 2b
a = 7 - 2(-3)
a = 7 + 6
[B]a = 13[/B]
[B](a, b) = (13, -3)[/B]

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will its dimensions be?
A flower bed has a rectangle shape, so the area is:
A = lw
We are given l = w + 3
Plugging in our numbers given to us, we have:
108 = w(w + 3)
w^2 + 3w = 108
Subtract 108 from each side:
w^2 + 3w - 108 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B3w-108%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get:
w = (9, -12)
Since length cannot be negative, w = 9.
And l = 9 + 3 --> l = 12
So we have [B](l, w) = (12, 9)[/B]
Checking our work, we have:
A = (12)9
A = 108 <-- Match!

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from sel

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?
Let the number of drinks be d. Let the number of salads be s. We're given two equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d + s = 209
[/LIST]
We can use substitution to solve this system of equations quickly. The question asks for the number of salads (s). Therefore, we want all expressions in terms of s. Rearrange Equation 2 by subtracting s from both sides:
d + s - s = 209 - s
Cancel the s's, we get:
d = 209 - s
So we have the following system of equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d = 209 - s
[/LIST]
Substitute equation (2) into equation (1) for d:
2(209 - s) + 6.50s = 836.50
Multiply through to remove the parentheses:
418 - 2s + 6.50s = 836.50
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=418-2s%2B6.50s%3D836.50&pl=Solve']type it into our search engine and we get[/URL]:
s = [B]93[/B]

A fruit basket contains 2 red apples and 2 green apples. What is the ratio of the number of red appl

A fruit basket contains 2 red apples and 2 green apples. What is the ratio of the number of red apples to the total number of apples?
2:2 = [B]1:1[/B] simplified

A furniture company plans to have 25 employees at its corporate headquarters and 25 employees at eac

A furniture company plans to have 25 employees at its corporate headquarters and 25 employees at each store it opens. Let s represent the number of stores and m represent the total number of employees.
There is only one corporate headquarters. So we have the number of employees (m) as:
m = Store Employees + Corporate Employees
Each store has 25 employees. Total store employees equal 25 per store times the number of stores (s).
[B]m = 25s + 25[/B]

A giant tortoise can live 175 years in captivity. The gastrotrich, which is a small aquatic animal,

A giant tortoise can live 175 years in captivity. The gastrotrich, which is a small aquatic animal, has a life-span of only 3 days (72 hours). If a gastrotrich died after 36 hours, a giant tortoise that lived 87.5 yeas would live proportionally the same because they both would have died halfway through their life-span.
How long would a giant tortoise live if it lived proportionally the same as a gastrotrich that died after 50 hours?
Set up a proportion of hours lived to lifespan where n is the number of years the giant tortoise lives:
50/72 = n/175
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=50&num2=n&den1=72&den2=175&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
n = [B]121.5[/B]

A group of 30 students from your school is part of the audience for a TV game show. The total number

A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience is 120. What theoretical probability of 5 students from your school being selected as contestants out of 9 possible contestant spots?
We want the probability a student from your school is chosen out of total students times total ways to choose students from your school:
[U]a) P(5 students being selected):[/U]
5/30 * 4/(120 - 30)
5/30 * 4/90
20/2700
[URL='https://www.mathcelebrity.com/fraction.php?frac1=20%2F2700&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get:
1/135
[U]b) Total Ways 9 students can be picked from your school:[/U]
9/120
[URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F120&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get:
3/40
Divide a by b:
1/135 / 3/40
40/405
[URL='https://www.mathcelebrity.com/fraction.php?frac1=40%2F405&frac2=3%2F8&pl=Simplify']Simplifying[/URL], we get:
[B]8/81[/B]

A group of campers have 250 pounds of food. They plan to eat 12 pounds a day. How many days will it

A group of campers have 250 pounds of food. They plan to eat 12 pounds a day. How many days will it take them to eat the food. Write your answer in a linear equation.
Let the number of days be d. We have the following equation:
12d = 250
To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=12d%3D250&pl=Solve']type this equation in our search engine[/URL] and we get:
d = [B]20.833[/B]

A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A star

A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A started with 6000 cells and decreased at a constant rate of 2000 cells per hour after the chemical was applied. Strain B started with 2000 cells and decreased at a constant rate of 1000 cells per hour after the chemical was applied. When will the strains have the same number of cells? Explain.
Set up strain equations where h is the number of hours since time 0:
[LIST]
[*]Strain A: 6000 - 2000h
[*]Strain B: 2000 - 1000h
[/LIST]
Set them equal to each other
6000 - 2000h = 2000 - 1000h
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=6000-2000h%3D2000-1000h&pl=Solve']equation solver[/URL], we see that [B]h = 4[/B]

A gym has yoga classes. Each class has 11 students. If there are c classes, write an equation to rep

A gym has yoga classes. Each class has 11 students. If there are c classes, write an equation to represent the total number of students s taking yoga.
Total students is the number of classes times the number of students in each class:
[B]s = 11c[/B]

A gym has yoga classes. Each class has 14 students. If there are c classes write an equation to repr

A gym has yoga classes. Each class has 14 students. If there are c classes write an equation to represent the total number of students s taking yoga
s = students per class * number of classes
[B]s = 14c[/B]

A gym membership has a $50 joining fee plus charges $17 a month for m months

A gym membership has a $50 joining fee plus charges $17 a month for m months
Build a cost equation C(m) where m is the number of months of membership.
C(m) = Variable Cost * variable units + Fixed Cost
C(m) = Months of membership * m + Joining Fee
Plugging in our numbers and we get:
[B]C(m) = 17m + 50
[MEDIA=youtube]VGXeqd3ikAI[/MEDIA][/B]

A heating company charges $60 per hour plus $54 for a service call. Let n be the number of hours t

A heating company charges $60 per hour plus $54 for a service call. Let n be the number of hours the technician works at your house.
The cost function C(n) where n is the number of hours is:
C(n) = Hourly Rate * hours + Service Call Charge
[B]C(n) = 60n + 54[/B]

A helicopter blade does 3206 full turns in 7 minutes , work out the number of full turns per minute

A helicopter blade does 3206 full turns in 7 minutes , work out the number of full turns per minute
3206 full turns / 7 minutes
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3206%2F7&frac2=3%2F8&pl=Simplify']Divide the fraction by 7 to get turns per minute[/URL]
[B]458 turns per minute[/B]

A hexagon has a total 126 dots and a equal number of dots on each side. how many dots on each side?

A hexagon has a total 126 dots and a equal number of dots on each side. how many dots on each side?
Since it has an equal number of dots on each side, each side has:
Number of dots on each side = 126 dots / 6 sides
Number of dots on each side = [B]21 dots per side[/B]

A high school graduating class is made up of 440 students. There are 168 more girls than boys. How m

A high school graduating class is made up of 440 students. There are 168 more girls than boys. How many boys are in the class?
Let b be the number of boys and g be the number of girls. We're given 2 equations:
[LIST=1]
[*]b + g = 440
[*]g = b + 168
[/LIST]
Substitute (2) into (1)
b + (b + 168) = 440
Combine like terms:
2b + 168 = 440
[URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B168%3D440&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]b = 136[/B]

A hot air balloon at 1120 feet descends at a rate of 80 feet per minute. Let y represent the height

A hot air balloon at 1120 feet descends at a rate of 80 feet per minute. Let y represent the height and let x represent the number of minutes the balloon descends.
Descending means we subtract height, so we have:
[B]y = 1120 - 80x[/B]

A hot dog costs $3 and a corn dog costs $1.50. If $201 was collected, write a mathematical sentence

A hot dog costs $3 and a corn dog costs $1.50. If $201 was collected, write a mathematical sentence to represent this information
Assumptions:
[LIST]
[*]Let the number of corn dogs be c
[*]Let the number of hot dogs be h
[/LIST]
Since cost = price * quantity, we have:
[B]1.50c + 3h = 201[/B]

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. How long is a job for which companies will charge the same amount?
Set up the cost function C(h) where h is the number of hours.
Company 1:
C(h) = 12h + 376
Company 2:
C(h) = 15h + 280
To see when the companies charge the same amount, set both C(h) functions equal to each other.
12h + 376 = 15h + 280
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B376%3D15h%2B280&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]32[/B]

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. How long is a job for which both companies will charge the same amount?
[U]Set up the cost function for the first company C(h) where h is the number of hours:[/U]
C(h) = Hourly Rate * h + flat rate
C(h) = 12h + 376
[U]Set up the cost function for the first company C(h) where h is the number of hours:[/U]
C(h) = Hourly Rate * h + flat rate
C(h) = 15h + 280
The problem asks how many hours will it take for both companies to charge the same. So we set the cost functions equal to each other:
12h + 376 = 15h + 280
Plugging this equation [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B376%3D15h%2B280&pl=Solve']into our search engine and solving for h[/URL], we get:
h = [B]32[/B]

A house rental company charges a $700 for a week stay plus an additional $4 per night for a roll awa

A house rental company charges a $700 for a week stay plus an additional $4 per night for a roll away bed. Your family rents a house for a week and pays $756. How many roll away beds did they rent?
Roll Away Beds = (Total Rental Price - Weekly Charge)/Per night bed fee
Plugging in our numbers, we get:
Roll Away Beds = (756 - 700)/4
Roll Away Beds = 56/4
Roll Away Beds = [B]14[/B]

A house valued at 70,000 in 1989 increased in value to 125,000 in 2000. Find a function which gives

A house valued at 70,000 in 1989 increased in value to 125,000 in 2000. Find a function which gives the value of the house, v, as a function of y, the number of years after 1989.
Let's determine the years:
2000 - 1989 = 11
Let's determine the change in value:
125,000 - 70,000 = 55,000
Assuming a linear progression, we have:
55,000/11 = 5,000 per year increase
[B]y = 70,000 + 5,000v[/B] where v is the number of years after 1989
Plug in 11 to check our work
y = 70,000 + 5,000(11)
y = 70,000 + 55,000
y = 125,000

A is 0 and AR=19 what is the midpoint

A is 0 and AR=19 what is the midpoint
[URL='https://www.mathcelebrity.com/mptnline.php?ept1=0&empt=&ept2=19&pl=Calculate+missing+Number+Line+item']Using our midpoint calculator, with one point at 0, and the other point at 19[/URL], we get the midpoint M:
M = [B]19/2 or 9.5[/B]

A is the set of odd integers between 4 and 12

A is the set of odd integers between 4 and 12
Let A be the set of odd numbers between 4 and 12:
[B]A = {5, 7, 9, 11}[/B]

a large fry has 120 more calories than a small. 5 large fries is the same amount of calories as 7 sm

a large fry has 120 more calories than a small. 5 large fries is the same amount of calories as 7 small. How many calories does each size fry have?
Let the number of calories in large fries be l. Let the number of calories in small fries be s. We're given two equations:
[LIST=1]
[*]l = s + 120
[*]5l = 7s
[/LIST]
Substitute equation (1) into equation (2):
5(s + 120) = 7s
[URL='https://www.mathcelebrity.com/1unk.php?num=5%28s%2B120%29%3D7s&pl=Solve']Type this equation into the search engine[/URL] and we get:
s = [B]300[/B]
Substitute s = 300 into equation (1):
l = 300 + 120
l = [B]420[/B]

A large storage container is filled with 44.9 quarts of water. One quart of water is equivalent to 3

A large storage container is filled with 44.9 quarts of water. One quart of water is equivalent to 32 fluid ounces. How many fluid ounces of water are stored in the container? Round your answer to the nearest whole number.
44.9 quarts * 32 fluid ounce / quart = 1,436.8
if we found to the nearest whole number, we round up since 0.8 is greater than 0.5, so we get:
[B]1,437 fluid ounces[/B]

a licence plate that has 3 numbers from 0 to 9 followed by 2 letters

a licence plate that has 3 numbers from 0 to 9 followed by 2 letters
How many license plate combinations can we form?
We multiply as follows:
[LIST]
[*][0-9] = 10 possible digits (D)
[*]A-Z = 26 possible letters (L)
[/LIST]
The problem asks for this:
DDDLL
So we have:
10 * 10 * 10 * 26 * 26 = [B]676,000[/B] plates

a license plate has 3 letters followed by 4 numbers

a license plate has 3 letters followed by 4 numbers
There are 26 letters A-Z and 10 numbers 0-9. So we have:
26 * 26 * 26 * 10 * 10 * 10 * 10
[B]175,760,000 different license plate combinations[/B]

A license plate is made up of 2 letter and 3 single digit numbers

A license plate is made up of 2 letter and 3 single digit numbers.
There are 26 letters (A-Z). And there are 10 single digit numbers [0-9]. So our total combinations are:
Letter - Letter - Number - Number - Number
26 * 26 * 10 * 10 * 10 = [B]676,000[/B]

A light bulb consumes 17100 watt-hours in 4 days and 18 hours. How many watt-hours does it consume a

A light bulb consumes 17100 watt-hours in 4 days and 18 hours. How many watt-hours does it consume a day?
Since one day equals 24 hours, we have:
4 days and 18 hours equals:
4(24) + 18 hours
96 + 18 hours
114 hours
Therefore, we have a proportion, where w is the number of watt-hours in a 24-hour period.
17,100 watt-hours/114 hours = w/24
[URL='https://www.mathcelebrity.com/prop.php?num1=17100&num2=w&den1=114&den2=24&propsign=%3D&pl=Calculate+missing+proportion+value']Typing 1711/114 = w/24 into our calculator[/URL], we get:
[B]w = 3,600[/B]

A light flashes every 2 minutes a, second light flashes every 7 minutes, and a third light flashes e

A light flashes every 2 minutes a, second light flashes every 7 minutes, and a third light flashes every 8 minutes. If all lights flash together at 8 P.M., what is the next time of day they will all flash together
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=2&num2=7&num3=8&pl=LCM']We use our least common multiple calculator[/URL] to see when the 3 numbers have a common multiple:
LCM of (2, , 8) = 56 minutes
So this means we add 56 minutes to 8:00 P.M. and we get [B]8:56 P.M.[/B]

a lighthouse blinks every 12 minutes. A second lighthouse blinks every 10 minutes if they both blink

a lighthouse blinks every 12 minutes. A second lighthouse blinks every 10 minutes if they both blink at 8:10 P.M at what time will they next blink together
We want the least common multiple of (10, 12). This will be the next time each number times a multiple equals the same number.
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=10&num2=12&num3=&pl=GCF+and+LCM']Typing in LCM 10,12 into our search engine[/URL], we get:
60
So if we start at 8:10, and 60 minutes later is when both lighthouses blink. 60 minutes equals 1 hour.
So we add 1 hour to 8:10, we have [B]9:10[/B]

A limo costs $85 to rent for 3 hours plus a 7% sales tax. What is the total cost to rent the limo fo

A limo costs $85 to rent for 3 hours plus a 7% sales tax. What is the total cost to rent the limo for 6 hours?
Determine the number of 3 hour blocks:
3 hour blocks = Total Rental Time / 3
3 hour blocks = 6 hours / 3
3 hour blocks = 2
With 7% = 0.07, we have:
Total Cost = $85 * / 3 hours * 2 (3 hour blocks) * 1.07
Total Cost = 85 * 2 * 1.07
Total Cost = [B]181.9[/B]

A local bank charges 19 per month plus 3 cents per check. The credit union charges7 per month plus

A local bank charges 19 per month plus 3 cents per check. The credit union charges7 per month plus 7 cents per check. How many checks should be written each month to make the credit union a better deal?
Set up the cost function B(c) for the local bank where c is the number of checks:
B(c) = 0.03c + 19
Set up the cost function B(c) for the credit union where c is the number of checks:
B(c) = 0.07c + 7
We want to find out when:
0.07c + 7 < 0.03c + 19
[URL='https://www.mathcelebrity.com/1unk.php?num=0.07c%2B7%3C0.03c%2B19&pl=Solve']Typing this inequality into our search engine[/URL], we get:
c < 300

A local Dunkin’ Donuts shop reported that its sales have increased exactly 16% per year for the last

A local Dunkin’ Donuts shop reported that its sales have increased exactly 16% per year for the last 2 years. This year’s sales were $80,642. What were Dunkin' Donuts' sales 2 years ago?
Declare variable and convert numbers:
[LIST]
[*]16% = 0.16
[*]let the sales 2 years ago be s.
[/LIST]
s(1 + 0.16)(1 + 0.16) = 80,642
s(1.16)(1.16) = 80,642
1.3456s = 80642
Solve for [I]s[/I] in the equation 1.3456s = 80642
[SIZE=5][B]Step 1: Divide each side of the equation by 1.3456[/B][/SIZE]
1.3456s/1.3456 = 80642/1.3456
s = 59930.142687277
s = [B]59,930.14[/B]

A local radio station sells time slots for programs in 20-minute intervals. If the station operates

A local radio station sells time slots for programs in 20-minute intervals. If the station operates 24 hours per day, what is the total number of 20-minute time slots the radio station can sell for Thursday and Friday?
Thursday and Friday = 2 days
With 24 hours per day, we have 24 * 2 = 48 hours for Thursday and Friday.
Since 20 minutes is 1/3 of an hour, then we have 3 20-minute time slots per hour.
3 20-minute time slots * 48 hours = [B]144[/B] total 20-minute time slots

A local shop sold 499 hamburgers and cheese burgers. There were 51 fewer cheese burgers sold. How ma

A local shop sold 499 hamburgers and cheese burgers. There were 51 fewer cheese burgers sold. How many hamburgers were sold?
Let h = number of hamburgers sold and c be the number of cheeseburgers sold.
We have two equations:
(1) c = h - 51
(2) c + h = 499
Substitute (1) into (2)
h - 51 + h = 499
Combine like terms
2h - 51 = 499
Add 51 to both sides
2h = 550
Divide each side by 2 to isolate h
[B]h = 275[/B]

A local sports centre charges $8 per visit. For an annual membership fee of$45, the cost per visit i

A local sports centre charges $8 per visit. For an annual membership fee of$45, the cost per visit is only $5.50. What is the least number of visits needed in a year in order for the membership to be a better deal?
Set up the cost for the visitors plan C(v) where v is the number of visits:
C(v) = 8v
Set up the cost for the membership plan C(v) where v is the number of visits:
C(v) = 5v + 45
The problem asks for v where:
5v + 45 < 8v
[URL='https://www.mathcelebrity.com/1unk.php?num=5v%2B45%3C8v&pl=Solve']Type this inequality into our search engine[/URL] and get:
v > 15
This means, the least number of visits is 1 more which is [B]16[/B]

A lottery uses a container with 25 identical balls numbered 1 through 25, from which three balls are

A lottery uses a container with 25 identical balls numbered 1 through 25, from which three balls are selected. What is the theoretical probability that the number 13 is picked first?
P(1st ball being 13) = [B]1 /25[/B]

A luncheon for 14 guests cost $468.00. What was the average cost per guest?

A luncheon for 14 guests cost $468.00. What was the average cost per guest?
Average Cost per Guest = Total Cost / Number of Guests
Average Cost per Guest = $468 / 14
Average Cost per Guest = [B]$33.43[/B]

A machine prints 230 movie posters each hour. Write and solve an equation to find the number of hour

A machine prints 230 movie posters each hour. Write and solve an equation to find the number of hours it takes the machine to print 1265 posters.
Let h be the number of hours. We're given the following expression for the printing output of the machine:
230h
The questions asks for how long (h) to print 1265 posters, so we setup the equation:
230h = 1265
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=230h%3D1265&pl=Solve']type this equation into our math engine[/URL] and we get:
h = [B]5.5 hours[/B]

A mail courier charges a base fee of $4.95 plus $11.90 per package being delivered. If x represents

A mail courier charges a base fee of $4.95 plus $11.90 per package being delivered. If x represents the number of packages delivered, which of the following equations could be used to find y, the total cost of mailing packages?
Set up the cost function y = C(x)
[B]C(x) = 4.95 + 11.90x[/B]

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket?
Declare variables:
[LIST]
[*]Let a be the number of adult's tickets
[*]Let c be the number of children's tickets
[/LIST]
Cost = Price * Quantity
We're given two equations:
[LIST=1]
[*]a + c = 20
[*]15a + 10c = 225
[/LIST]
Rearrange equation (1) in terms of a:
[LIST=1]
[*]a = 20 - c
[*]15a + 10c = 225
[/LIST]
Now that I have equation (1) in terms of a, we can substitute into equation (2) for a:
15(20 - c) + 10c = 225
Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225
We first need to simplify the expression removing parentheses
Simplify 15(20 - c): Distribute the 15 to each term in (20-c)
15 * 20 = (15 * 20) = 300
15 * -c = (15 * -1)c = -15c
Our Total expanded term is 300-15c
Our updated term to work with is 300 - 15c + 10c = 225
We first need to simplify the expression removing parentheses
Our updated term to work with is 300 - 15c + 10c = 225
[SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE]
(-15 + 10)c = -5c
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
-5c + 300 = + 225
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 300 and 225. To do that, we subtract 300 from both sides
-5c + 300 - 300 = 225 - 300
[SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE]
-5c = -75
[SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE]
-5c/-5 = -75/-5
c = [B]15[/B]
Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a:
a = 20 - 15
a = [B]5[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produced. The product sells for $20/unit
[U]Cost Function C(u) where u is the number of units:[/U]
C(u) = cost per unit * u + fixed cost
C(u) = 12u + 100000
[U]Revenue Function R(u) where u is the number of units:[/U]
R(u) = Sale price * u
R(u) = 20u
Break even point is where C(u) = R(u):
C(u) = R(u)
12u + 100000 = 20u
To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=12u%2B100000%3D20u&pl=Solve']type this equation into our search engine[/URL] and we get:
u = [B]12,500[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produced. The product sells for $20/unit.
Let u be the number of units. We have a cost function C(u) as:
C(u) = Variable cost * u + Fixed Cost
C(u) = 14u + 100000
[U]We have a revenue function R(u) with u units as:[/U]
R(u) = Sale Price * u
R(u) = 20u
[U]We have a profit function P(u) with u units as:[/U]
Profit = Revenue - Cost
P(u) = R(u) - C(u)
P(u) = 20u - (14u + 100000)
P(u) = 20u - 14u - 100000
P(u) = 6u - 1000000

A Math Quiz has 5 multiple choice option. Each question has four options. Find the number of possibl

[SIZE=6][B]A quiz has 5 questions with 4 answer choices each find the number of possible outcomes[/B]
[B][/B]
[B]We have 4 * 4 * 4 * 4 * 4 = 1024 outcomes[/B][/SIZE]

A math teacher bought 40 calculators at $8.20 each and a number of other calculators costing$2.95 ea

A math teacher bought 40 calculators at $8.20 each and a number of other calculators costing$2.95 each. In all she spent $387. How many of the cheaper calculators did she buy
Let the number of cheaters calculators be c. Since amount equals price * quantity, we're given the following equation:
8.20 * 40 + 2.95c = 387
To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=8.20%2A40%2B2.95c%3D387&pl=Solve']type it in our search engine [/URL]and we get:
c = [B]20[/B]

A Math teacher gives one test a week to his class of 31 students. Estimate the number of tests the t

A Math teacher gives one test a week to his class of 31 students. Estimate the number of tests the teacher will mark in 39 weeks.
31 students * 1 test per week * 39 weeks = [B]1,209 tests[/B]

A mechanic charges $45 per hour and parts cost $125. Write an expression for the total if the mechan

A mechanic charges $45 per hour and parts cost $125. Write an expression for the total if the mechanic works h hours.
Set up the cost function C(h) where h is the number of hours worked:
C(h) = Hourly Rate * h + parts
C(h) = [B]45h + 125[/B]

A mechanic will charge a new customer $45.00 for an initial diagnosis plus $20 an hour of labor. How

A mechanic will charge a new customer $45.00 for an initial diagnosis plus $20 an hour of labor. How long did the mechanic work on a car if he charged the customer $165?
We set up a cost function C(h) where h is the number of hours of labor:
C(h) = Hourly Labor Rate * h + Initial Diagnosis
C(h) = 20h + 45
The problem asks for the number of hours if C(h) = 165. So we set our cost function C(h) above equal to 165:
20h + 45 = 165
To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B45%3D165&pl=Solve']we plug this equation into our search engine[/URL] and we get:
h = [B]6[/B]

A members-only speaker series allows people to join for $16 and then pay $1 for every event attended

A members-only speaker series allows people to join for $16 and then pay $1 for every event attended. What is the maximum number of events someone can attend for a total cost of $47?
Subtract the join fee from the total cost:
$47 - $16 = $31
Now divide this number by the cost per event:
$31 / $1 = [B]31 events[/B]

A milk booth sells 445 litres of milk in a day. How many litres of milk will it sell in 4 years

A milk booth sells 445 litres of milk in a day. How many litres of milk will it sell in 4 years
Calculate the number of days in 4 years:
Days in 4 years = Days in 1 year * 4
Days in 4 years = 365 * 4
Days in 4 years = 1,460
Calculate litres of milk sold in 4 years:
Litres of milk sold in 4 years = Litres of milk sold in 1 day * Days in 4 years
Litres of milk sold in 4 years = 445 * 1,460
Litres of milk sold in 4 years = [B]649,700 litres[/B]

A monster energy drink has 164 mg of caffeine. Each hour your system reduces the amount of caffeine

A monster energy drink has 164 mg of caffeine. Each hour your system reduces the amount of caffeine by 12%. Write an equation that models the amount of caffeine that remains in your body after you drink an entire monster energy.
Set up a function C(h) where he is the number of hours after you drink the Monster energy drink:
Since 12% as a decimal is 0.12, we have:
C(h) = 164 * (1 - 0.12)^h <-- we subtract 12% since your body flushes it out
[B]C(h) = 164 * (0.88)^h[/B]

A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age o

A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.
If the baby gains 5 pounds every 2 months, then they gain 5/2 = 2.5 pounds per month. Let x be the number of months old for the baby, we have:
The baby starts at 10 pounds. And every month (x), the baby's weight increases 2.5 pounds. Our equation is:
[B]y = 2.5x + 10[/B]

A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of

A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx b that describes the baby's weight.
The baby gains 4 pounds every month, where x is the number of months since birth. The baby boy starts life (time 0) at 6 pounds. So we have
[B]y = 4x + 6[/B]

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.
Every month, the baby gains 2/3 of a pound. So we have:
[B]y = 2/3x + 7
[/B]
The baby starts off with 7 pounds. So we add 7 pounds + 2/3 times the number of months passed since birth.

A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pa

A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pass for $80. How many days must he work (i.e. pass through the toll) in order to break even?
Let the number of days be d. Break even means both costs are equal. We want to find when:
4.75d = 80
To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.75d%3D80&pl=Solve']type this equation into our search engine[/URL] and we get:
d = 16.84 days
We round up to an even [B]17 days[/B].

A movie theater charges $7 for adults and $3 for seniors on a particular day when 324 people paid an

A movie theater charges $7 for adults and $3 for seniors on a particular day when 324 people paid an admission the total receipts were 1228 how many were seniors and how many were adults?
Let the number of adult tickets be a. Let the number of senior tickets be s. We're given two equations:
[LIST=1]
[*]a + s = 324
[*]7a + 3s = 1228
[/LIST]
We have a set of simultaneous equations we can solve using 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]a = 64[/B]
[*][B]s = 260[/B]
[/LIST]

A movie theater charges 7.00 for adults and 2.00 for seniors citizens. On a day when 304 people paid

A movie theater charges 7.00 for adults and 2.00 for seniors citizens. On a day when 304 people paid for admission, the total receipt were 1118. How many who paid were adults ? How many were senior citizens?
Let a be the number of adult tickets. Let s be the number of senior citizen tickets. We're given two equations:
[LIST=1]
[*]a + s = 304
[*]7a + 2s = 1118
[/LIST]
We can solve this system of equations three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Cramers+Method']Cramer's Method[/URL]
[/LIST]
No matter which way we choose, we end up with the same answer:
[LIST]
[*]a = [B]102[/B]
[*]s = [B]202[/B]
[/LIST]

A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for stu

A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1030, How many children, students, and adults attended?
Let c be the number of children's tickets, s be the number of student's tickets, and a be the number of adult's tickets. We have 3 equations:
[LIST=1]
[*]a + c + s = 143
[*]a = 0.5c
[*]12a + 5c + 7s =1030
[/LIST]
Substitute (2) into (1)
0.5c + c + s = 143
1.5c + s = 143
Subtract 1.5c from each side
4. s = 143 - 1.5c
Now, take (4) and (2), and plug it into (3)
12(0.5c) + 5c + 7(143 - 1.5c) = 1030
6c + 5c + 1001 - 10.5c = 1030
Combine like terms:
0.5c + 1001 = 1030
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.5c%2B1001%3D1030&pl=Solve']equation calculator[/URL] to get [B]c = 58[/B].
Plug this back into (2)
a = 0.5(58)
[B]a = 29
[/B]
Now take the a and c values, and plug it into (1)
29 + 58 + s = 143
s + 87 = 143
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B87%3D143&pl=Solve']equation calculator[/URL] again, we get [B]s = 56[/B].
To summarize, we have:
[LIST]
[*]29 adults
[*]58 children
[*]56 students
[/LIST]

A music app charges $2 to download the app plus $1.29 per song download. Write and solve a linear eq

A music app charges $2 to download the app plus $1.29 per song download. Write and solve a linear equation to find the total cost to download 30 songs
Set up the cost function C(s) where s is the number of songs:
C(s) = cost per song * s + download fee
Plugging in our numbers for s = 30 and a download fee of $2 and s = 1.29, we have:
C(30) = 1.29(30) + 2
C(30) = 38.7 + 2
C(30) = [B]40.7[/B]

A music app charges $2 to download the app plus $1.29 per song downloaded

A music app charges $2 to download the app plus $1.29 per song downloaded
Let d be the number of downloads. The cost function C(d) is:
C(d) = cost per download * d + download fee
[B]C(d) = 1.29d + 2[/B]

A music app charges $2 to download the app plus $1.29 per song downloaded. Write and solve a linear

A music app charges $2 to download the app plus $1.29 per song downloaded. Write and solve a linear equation to find the total cost to download 30 songs.
Let the number of songs be s. And the cost function be C(s). We have:
C(s) = Price per song downloaded * s + app download charge
C(s) = 1.29s + 2
The problem asks for C(30):
C(3) = 1.29(30) + 2
C(3) = 38.7 +2
C(3) = $[B]40.7[/B]

a music app charges $5 to download the app plus $1.25 per song downloaded. write linear equation to

a music app charges $5 to download the app plus $1.25 per song downloaded. write linear equation to calculate the cost for x number of songs
With x songs, our Cost equation C(x) is:
C(x) = cost per download * x downloads + app download fee
[B]C(x) = 1.25x + 5[/B]

A music app charges 2$ to download the app plus 1.29$ per song download. Write and solve linear equa

A music app charges 2$ to download the app plus 1.29$ per song download. Write and solve linear equation and a linear equation to find the total cost to download 30 songs
Set up the equation C(d) where d is the number of downloads:
C(d) = cost per download * d + download fee
Plugging in our numbers, we get:
C(d) = 1.29d + 2
The problem asks for C(30):
C(30) = 1.29(30) + 2
C(30) = 38.7 + 2
C(30) = [B]40.70[/B]

A natural number greater than 1 has only itself and 1 as factors is called

A natural number greater than 1 has only itself and 1 as factors is called a [B]prime number.[/B]

A necklace chain costs $15. Beads cost $2.75 each. You spend a total of $28.75 on a necklace and bea

A necklace chain costs $15. Beads cost $2.75 each. You spend a total of $28.75 on a necklace and beads before tax. How many beads did you buy in addition to the necklace?
[U]Calculate the amount left to spend on beads:[/U]
Bead Spend = Total Spend - Necklace Cost
Bead Spend = $28.75 - $15
Bead Spend = $13.75
[U]Calculate the number of beads you bought:[/U]
Beads Bought = Bead Spend / Cost Per Bead
Beads Bought = $13.75 / $2.75
Beads Bought = [B]$5[/B]

A new car worth $24,000 is depreciating in value by $3,000 per year , how many years till the cars v

A new car worth $24,000 is depreciating in value by $3,000 per year , how many years till the cars value will be $9,000
We have a flat rate depreciation each year. Set up the function D(t) where t is the number of years of depreciation:
D(t) = 24000 - 3000t
The problem asks for the time (t) when D(t) = 9000. So we set D(t) = 9000
24000 - 3000 t = 9000
To solve for t, [URL='https://www.mathcelebrity.com/1unk.php?num=24000-3000t%3D9000&pl=Solve']we plug this function into our search engine[/URL] and we get:
t = [B]5[/B]

A new car worth $30,000 is depreciating in value by $3,000 per year. After how many years will the c

A new car worth $30,000 is depreciating in value by $3,000 per year. After how many years will the cars value be $9,000
Step 1, the question asks for Book Value. Let y be the number of years since purchase.
We setup an equation B(y) which is the Book Value at time y.
B(y) = Sale Price - Depreciation Amount * y
We're given Sale price = $30,000, depreciation amount = 3,000, and B(y) = 9000
30000 - 3000y = 9000
To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=30000-3000y%3D9000&pl=Solve']type this in our math engine[/URL] and we get:
y = [B]7
[/B]
To check our work, substitute y = 7 into B(y)
B(7) = 30000 - 3000(7)
B(7) = 30000 - 21000
B(7) = 9000
[MEDIA=youtube]oCpBBS7fRYs[/MEDIA]

A new company is projecting its profits over a number of weeks. They predict that their profits each

A new company is projecting its profits over a number of weeks. They predict that their profits each week can be modeled by a geometric sequence.
Three weeks after they started, the company's projected profit is $10,985.00
Four weeks after they started, the company's projected profit is $14,280.50
Let Pn be the projected profit, in dollars, n weeks after the company started tracking their profits.
a. What is the common ratio of the sequence?
b. Calculate the initial value
c. Construct a recurrence relation that can be used to model the value of Pn
a. 14,280.50/10,985.00 = [B]1.3[/B]
b. 3 weeks ago, the Initial value is 10,985/1.3^3 = [B]$5,000
c. Pn = 5000 * 1.3^n[/B]

a number added to 5 minus p

a number added to 5 minus p
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We add 5 minus p to this number x:
[B]x + 5 - p[/B]

a number added to the product of y and x

a number added to the product of y and x
Since we're already using the variables x and y, we choose another arbitrary variable for the phrase [I]a number.[/I]
a
The product of y and x isL
xy
Then add a:
[B]a + xy[/B]

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the pro

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 3 and the coin toss is heads? Write your answer as a fraction in simplest form
Let's review the vitals of this question:
[LIST]
[*]The probability of heads on a fair coin is 1/2.
[*]On a fair die, greater than 3 means either 4, 5, or 6. Any die roll face is a 1/6 probability.
[*]So we have a combination of outcomes below:
[/LIST]
Outcomes
[LIST=1]
[*]Heads and 4
[*]Heads and 5
[*]Heads and 6
[/LIST]
For each of the outcomes, we assign a probability. Since the coin flip and die roll are independent, we multiply the probabilities:
[LIST=1]
[*]P(Heads and 4) = 1/2 * 1/6 = 1/12
[*]P(Heads and 5) = 1/2 * 1/6 = 1/12
[*]P(Heads and 6) = 1/2 * 1/6 = 1/12
[/LIST]
Since we want any of those events, we add all three probabilities
1/12 + 1/12 + 1/12 = 3/12
This fraction is not simplified. S[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F12&frac2=3%2F8&pl=Simplify']o we type this fraction into our search engine, and choose Simplify[/URL].
We get a probability of [B]1/4[/B].
By the way, if you need a decimal answer or percentage answer instead of a fraction, we type in the following phrase into our search engine:
[URL='https://www.mathcelebrity.com/perc.php?num=1&den=4&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']1/4 to decimal[/URL]
Alternative Answers:
[LIST]
[*]For a decimal, we get [B]0.25[/B]
[*]For a percentage, we get [B]25%[/B]
[/LIST]

a number increased by 8 and then tripled

a number increased by 8 and then tripled
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Increased by 8 means we add 8 to x:
x + 8
Then tripled means we multiply the expression x + 8 by 3:
[B]3(x + 8)[/B]

a number is twice another number

a number is twice another number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
The phrase [I]another number [/I]means another arbitrary variable, let's call it y
Twice means we multiply y by 2:
2y
The phrase [I]is [/I]means an equation, so we set x equal to 2y:
[B]x = 2y[/B]

A number K is doubled and then increased by 3

A number K is doubled and then increased by 3
K is doubled means we multiply K by 2:
2K
Increased by 3 means we add:
[B]2K + 3[/B]

A number m is no less than -8 and fewer than 9.

A number m is no less than -8 and fewer than 9.
No less than means greater than or equal to:
m >= -8
Fewer than 9 means less than 9:
m < 9
Combine these two inequalities to get
[B]-8 <= m < 9[/B]

A number multiplied by 6 and divided by 5 give four more than a number?

A number multiplied by 6 and divided by 5 give four more than a number?
A number is represented by an arbitrary variable, let's call it x.
Multiply by 6:
6x
Divide by 5
6x/5
The word "gives" means equals, so we set this equal to 4 more than a number, which is x + 4.
6x/5 = x + 4
Now, multiply each side of the equation by 5, to eliminate the fraction on the left hand side:
6x(5)/5 = 5(x + 4)
The 5's cancel on the left side, giving us:
6x = 5x + 20
Subtract 5x from each side
[B]x = 20[/B]
Check our work from our original equation:
6x/5 = x + 4
6(20)/5 ? 20 + 4
120/5 ?24
24 = 24 <-- Yes, we verified our answer

A number n diminished by 8 gives 12

A number n diminished by 8 gives 12
A number n can be written as n:
n
Diminished by means we subtract, so we subtract 8 from n:
n - 8
The word [I]gives[/I] means an equation, so we set n - 8 equal to 12:
[B]n - 8 = 12[/B]

A number n is no less than 2 and no more than 49.

A number n is no less than 2 and no more than 49.
This is a compound inequality. Let's break it into parts.
Step 1: No more than 49 means 49 or less. Or, less than or equal to 49
<= 49
Step 2: no less than 2 means 2 or greater. Or, greater than or equal to 2
>=2
Writing this in terms of the number n, we have:
[B]2 <= n <= 49[/B]

a number of bacteria b tripled

a number of bacteria b tripled
The word [I]tripled[/I] means we multiply by 3, so we have:
[B]3b[/B]

A number of dogs are to equally share a bag of dog food. If there are n dogs in the group and one do

A number of dogs are to equally share a bag of dog food. If there are [I]n[/I] dogs in the group and one dog eats its share, what percent of the bag is left?
Fraction of the bag left is:
(n - 1)/n
Multiply by 100 to get a percentage:
[B]100(n - 1)/n[/B]

a number of pennies splits into 4 equal groups

a number of pennies splits into 4 equal groups
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take x and divide it by 4 to get 4 equal groups:
[B]x/4[/B]

a number of seconds in 50 minutes

a number of seconds in 50 minutes
60 seconds / minute * 50 minutes = 60 * 50 seconds = [B]3,000 seconds[/B]

A number p subtracted by its double is 10

A number p subtracted by its double is 10
The double of a number means we multiply p by 2:
2p
A number p is subtracted by its double
p - 2p
The phrase [I]is[/I] means equal to, so we set p - 2p equal to 10:
[B]p - 2p = 10[/B]

A number t is no less than 30 and fewer than 40.

A number t is no less than 30 and fewer than 40.
This is a compound inequality. Take it in 3 parts:
Step 1: fewer than 40 means less than (does not include 40)
t < 40
Step 2: no less than 30 means greater than or equal to
t >= 30
Step 3: Combine these 2 statements into one compound inequality:
[B]30 <= t < 40[/B]

A number y increased by itself

A number y increased by itself
increased by itself means we add the variable y to itself to get our final algebraic expression of:
[B]y + y
[/B]
[I]If[/I] the problem asks you to simplify, we group like terms and get:
[B]2y[/B]

A numerical pass code is required to open a car door. The pass code is five digits long and uses the

A numerical pass code is required to open a car door. The pass code is five digits long and uses the digits 0-9. Numbers may be repeated in the pass code. How many different pass codes exist?
0-9 is 10 digits. Since digits can repeat, we use the fundamental rule of counting to get:
10 * 10 * 10 * 10 * 10 = [B]100,000 different pass codes[/B]

a package of soccer accessories costs $25 for cleats, $14 for shin guards , and $12 for a ball. Writ

a package of soccer accessories costs $25 for cleats, $14 for shin guards , and $12 for a ball. Write two equivalent expressions for the total cost of 9 accessory package. Then find the cost.
Let c be the number of cleats, s be the number of shin guards, and b be the number of balls. We have the following cost function for 9 accessory packages:
[B]9(25c + 14s + 12b)[/B]
But if we multiply through, we get an equivalent expression:
[B]225c + 126s + 108b[/B]

A package that is heavier than 11 lbs and 8 oz will have a label that says HEAVY on it. Gloria packe

A package that is heavier than 11 lbs and 8 oz will have a label that says HEAVY on it. Gloria packed 6 flowerpots to send to her customers. Each of the flowerpots weighs 1 lb and 12 oz. The packing material weighs 5 oz. Will her package be labeled as HEAVY?
Calculate weight of flowerpots:
Flowerpot weight = Weight per flowerpot * number of flowerpots
Flowerpot weight = 1 lb 12 oz * 6
Flowerpot weight = 6 lb and 72 oz
Since 72oz = 72/16 = 4 lbs and 8 oz, we have:
Flowerpot weight = 6 lb 8 oz + 4 lbs and 8 oz = 12 lb 16 oz
Since 16oz = 1 lb, we have:
13lb
Add in the 5 oz of packing material, we have:
13lb 5 oz
Since this is greater than 11lb 8oz, the package [B]will be labeled as HEAVY[/B]

A packing machine can package 236 first aid kit each hour. At this rate, find the number of first ai

A packing machine can package 236 first aid kit each hour. At this rate, find the number of first aid kit package in 24 hours
Total First Aid Kits = Kits Per Hour * Number of Hours
Total First Aid Kits = 236 * 24
Total First Aid Kits = [B]5,664[/B]

A pair of numbers has an HCF (Highest Common Factor) of 3, and an LCM (Lowest Common Multiple) of

A pair of numbers has an HCF (Highest Common Factor) of 3, and an LCM (Lowest Common Multiple) of 45 . If one of the numbers in the pair is 15 , what is the other number?
[LIST=1]
[*]Prime Factorization for 15 is 3 * 5
[*]Prime Factorization for 9 is 3 * 3
[*]LCM of (9, 15) = 35
[/LIST]
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=9&num2=15&num3=&pl=GCF+and+LCM']Check out this link here to see the details[/URL]

A pair of standard dice is rolled, how many possible outcomes are there

A pair of standard dice is rolled, how many possible outcomes are there?
We want the number of outcomes in the sample space.
The first die has 6 possibilities 1-6.
The second die has 6 possibilities 1-6.
Our sample space count is 6 x 6 = [B]36 different outcomes
[/B]
[LIST=1]
[*](1, 1)
[*](1, 2)
[*](1, 3)
[*](1, 4)
[*](1, 5)
[*](1, 6)
[*](2, 1)
[*](2, 2)
[*](2, 3)
[*](2, 4)
[*](2, 5)
[*](2, 6)
[*](3, 1)
[*](3, 2)
[*](3, 3)
[*](3, 4)
[*](3, 5)
[*](3, 6)
[*](4, 1)
[*](4, 2)
[*](4, 3)
[*](4, 4)
[*](4, 5)
[*](4, 6)
[*](5, 1)
[*](5, 2)
[*](5, 3)
[*](5, 4)
[*](5, 5)
[*](5, 6)
[*](6, 1)
[*](6, 2)
[*](6, 3)
[*](6, 4)
[*](6, 5)
[*](6, 6)
[/LIST]

a paper boy delivers thirteen paper to an apartment complex. if these deliveries compose one-seventh

a paper boy delivers thirteen paper to an apartment complex. if these deliveries compose one-seventh of his route, how many papers does he deliver
Let d be the total number of deliveries the paper boy makes on the route.
d
We're given, d/7 = 13
d = 13 * 7
d = [B]91
[MEDIA=youtube]HRviz-3fn5c[/MEDIA][/B]

A parking lot has seventy-one parking spaces numbered from 1 to 71. There are no cars in the parking

A parking lot has seventy-one parking spaces numbered from 1 to 71. There are no cars in the parking lot when Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she parks is greater than or equal to 31?
Greater than or equal to means including 31 all the way through 71
31-71 is 40 spaces
P(s>=31) = [B]40/71[/B]

A parking lot has sixty-eight parking spaces numbered from 1 to 68. There are no cars in the parking

A parking lot has sixty-eight parking spaces numbered from 1 to 68. There are no cars in the parking lot when Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she parks is greater than or equal to 21?
We want P(X>=21). This is also found by taking 1 - P(X <= 20).
P(X<=20) = 20/68. Reduced using a [URL='http://www.mathcelebrity.com/gcflcm.php?num1=20&num2=68&num3=&pl=GCF']GCF of 4[/URL], we get 5/17.
P(X >=21) = 1 - 5/17 = [B]12/17[/B]

A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of

A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of each coin are there?
Let d = the number of dimes and q = the number of quarters. We have two equations:
(1) d + q = 146
(2) 0.1d + 0.25q = 27.05
Rearrange (1) into (3) solving for d
(3) d = 146 - q
Substitute (3) into (2)
0.1(146 - q) + 0.25q = 27.05
14.6 - 0.1q + 0.25q = 27.05
Combine q's
0.15q + 14.6 = 27.05
Subtract 14.6 from each side
0.15q = 12.45
Divide each side by 0.15
[B]q = 83[/B]
Plugging that into (3), we have:
d = 146 - 83
[B]d = 63[/B]

A peanut vendor has initial start up costs of $7600 and variable costs of $0.70 per bag of peanuts.

A peanut vendor has initial start up costs of $7600 and variable costs of $0.70 per bag of peanuts. What is the cost function?
We set up the cost function C(b) where b is the number of bags:
C(b) = Cost per bag * b + Start up costs
Plugging in our numbers, we get:
[B]C(b) = 0.70b + 7600[/B]

A person has $13,000 invested in stock A and stock B. Stock A currently sells for $20 a share and

A person has $13,000 invested in stock A and stock B. Stock A currently sells for $20 a share and stock B sells for $90 a share. If stock B triples in value and stock A goes up 50%, his stock will be worth $33,000. How many shares of each stock does he own?
Set up the given equations, where A is the number of shares for Stock A, and B is the number of shares for Stock B
[LIST=1]
[*]90A + 20B = 13000
[*]3(90A) + 1.5(20B) = 33000 <-- [I]Triple means multiply by 3, and 50% gain means multiply by 1.5[/I]
[/LIST]
Rewrite (2) by multiplying through:
270A + 30B = 33000
Using our simultaneous equations calculator, we get [B]A = 100 and B = 200[/B]. Click the links below to solve using each method:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]
Check our work using equation (1)
90(100) + 20(200) ? 13,000
9000 + 4000 ? 13,000
13000 = 13000

A person is earning 600 per day to do a certain job. Express the total salary as a function of the n

A person is earning 600 per day to do a certain job. Express the total salary as a function of the number of days that the person works.
Set up the salary function S(d) where d is the number of days that the person works:
S(d) = Daily Rate * d
[B]S(d) = 600d[/B]

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuou

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV = Pe^{rt} V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years.
Substituting our given numbers in where P = 96,300, r = 0.028, and t = 7, we get:
V = 96,300 * e^(0.028 * 7)
V = 96,300 * e^0.196
V = 96,300 * 1.21652690533
V = [B]$117,151.54[/B]

A person that runs for 15 minutes burns 180 calories. If someone burns 300 calories, how long did tg

A person that runs for 15 minutes burns 180 calories. If someone burns 300 calories, how long did tgey run for
Set up a proportion of minutes to calories where m is the number of minutes per 300 calories:
15/180 = m/300
To solve for m, [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=m&den1=180&den2=300&propsign=%3D&pl=Calculate+missing+proportion+value']we type this proportion into our search engine[/URL] and we get:
m = [B]25[/B]

A person will devote 31 years to be sleeping and watching tv. The number of years sleeping will exce

A person will devote 31 years to be sleeping and watching tv. The number of years sleeping will exceed the number of years watching tv by 19. How many years will the person spend on each of these activities
Let s be sleeping years and t be tv years, we have two equations:
[LIST=1]
[*]s + t = 31
[*]s = t + 19
[/LIST]
Substitute (2) into (1)
(t + 19) + t = 31
Combine like terms:
2t + 19 = 31
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2t%2B19%3D31&pl=Solve']equation solver[/URL], we get [B]t = 6[/B]. Using equation (2), we have
s = 6 + 19
s = [B]25[/B]

A Petri dish contains 2000. The number of bacteria triples every 6 hours. How many bacteria will exi

A Petri dish contains 2000. The number of bacteria triples every 6 hours. How many bacteria will exist after 3 days?
Determine the amount of tripling periods:
[LIST]
[*]There are 24 hours in a day.
[*]24 hours in a day * 3 days = 72 hours
[*]72 hours / 6 hours tripling period = 12 tripling periods
[/LIST]
Our bacteria population function B(t) where t is the amount of tripling periods. Tripling means we multiply by 3, so we have:
B(t) = 2000 * 3^t
with t = 12 tripling periods, we have:
B(12) = 2000 * 3^12
B(12) = 2000 * 531441
B(12) = [B]1,062,882,000[/B]

A photographer snapped 224 photos over a period of 15 days. At this rate, how many would he take in

A photographer snapped 224 photos over a period of 15 days. At this rate, how many would he take in 45 days?
Set up a proportion of photos to days where p is the number of photos snapped in 45 days:
224/15 = p/45
To solve this proportion for p, we [URL='https://www.mathcelebrity.com/prop.php?num1=224&num2=p&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get;
p = [B]672[/B]

A piggy bank contains $90.25 in dimes and quarters. Which equation represents this scenario? Let x r

A piggy bank contains $90.25 in dimes and quarters. Which equation represents this scenario? Let x represent the number of dimes, and let y represent the number of quarters.
Since amount = cost * quantity, we have:
[B]0.1d + 0.25q = 90.25[/B]

A pile of coins, consisting of quarters and half dollars, is worth 11.75. If there are 2 more quarte

A pile of coins, consisting of quarters and half dollars, is worth 11.75. If there are 2 more quarters than half dollars, how many of each are there?
Let h be the number of half-dollars and q be the number of quarters. Set up two equations:
(1) q = h + 2
(2) 0.25q + 0.5h = 11.75
[U]Substitute (1) into (2)[/U]
0.25(h + 2) + 0.5h = 11.75
0.25h + 0.5 + 0.5h = 11.75
[U]Group h terms[/U]
0.75h + 0.5 = 11.75
[U]Subtract 0.5 from each side[/U]
0.75h = 11.25
[U]Divide each side by h[/U]
[B]h = 15[/B]
[U]Substitute h = 15 into (1)[/U]
q = 15 + 2
[B]q = 17[/B]

A plant is 15 cm high and grows 4.5 cm every month. How many months will it take until the plant is

A plant is 15 cm high and grows 4.5 cm every month. How many months will it take until the plant is 27.5 cm
We set up the height function H(m) where m is the number of months since now. We have:
H(m) = 4.5m + 15
We want to know when H(m) = 27.5, so we set our H(m) function equal to 27.5:
4.5m + 15 = 27.5
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.5m%2B15%3D27.5&pl=Solve']type this equation into our search engine[/URL] and we get:
m = 2.78
So we round up to [B]3 whole months[/B]

A playground requires 2,459 pounds of sand to cover the ground. If the sand comes in 60-pound bags,

A playground requires 2,459 pounds of sand to cover the ground. If the sand comes in 60-pound bags, how many bags are needed
Number of bags = Total Weight of Sand / Pounds per bag
Number of bags = 2459/60
Number of bags = 40.9833

A plumber charges $45 for a house call plus $25 for each hour worked.Let h represent the number of h

A plumber charges $45 for a house call plus $25 for each hour worked.Let h represent the number of hours worked. Write the expression that shows how much a plumber charges for a job. Then find how much the plumbers charges for a job lasting 4 hours
[U]Set up the cost function C(h) where h is the number of hours:[/U]
C(h) = Hours worked * hourly rate + house call fee
[B]C(h) = 25h + 45 <-- This is the expression for how much the plumber charges for a job
[/B]
[U]Now determine how much the plumber charges for a job lasting 4 hours[/U]
We want C(4)
C(4) = 25(4) + 45
C(4) = 100 + 45
C(4) = [B]$145[/B]

A plumber makes a starting $36,000 a year. They get paid semimonthly. They have a health insurance p

A plumber makes a starting $36,000 a year. They get paid semimonthly. They have a health insurance premium of $74.28 and $25 in union dues each paycheck. 1. What is their semimonthly salary?
Calculate the number of semi-monthly periods per year:
Semi-monthly periods per year = 12 Months per year * 2
Semi-monthly periods per year = 24
Calculate semi-monthly salary amount:
Semi-monthly salary amount = Annual Salary / Semi-monthly periods per year
Semi-monthly salary amount = $36,000 / 24
Semi-monthly salary amount = $1,500
Now, calculate the net pay each semimonthly period:
Net pay = Semi-monthly salary amount - Health Insurance Premium - Union Dues
Net pay = $1,500 - $74.28 - $25
Net pay = [B]$1,400.72[/B]

A pot of soup, currently 66°C above room temperature, is left out to cool. If that temperature diffe

A pot of soup, currently 66°C above room temperature, is left out to cool. If that temperature difference decreases by 10% per minute, then what will the difference be in 17 minutes?
We set up the temperature function T(m), where m is the number of minutes of cooling. With 10% = 0.1, we have:
T(m) = 66 * (1 - 0.10)^m
The problem asks for T(17) [U]and[/U] the difference temperature:
T(17) = 66 * 0.9^17
T(17) = 66 * 0.16677181699
T(17) = [B]11.01C[/B]
[B][/B]
[U]Calculate the difference in temperature[/U]
Difference = Starting Temperature - Ending Temperature
Difference = 66 - 11.01
Difference = 66 - 11.01 = [B]54.99 ~ 55[/B]

A pound of chocolate costs 7 dollars. Hong buys p pounds . Write an equation to represent the total

A pound of chocolate costs 7 dollars. Hong buys p pounds . Write an equation to represent the total cost c that Hong pays
Our equation is the cost of chocolate multiplied by the number of pounds:
[B]c = 7p[/B]

A pretzel factory has daily fixed costs of $1100. In addition, it costs 70 cents to produce each bag

A pretzel factory has daily fixed costs of $1100. In addition, it costs 70 cents to produce each bag of pretzels. A bag of pretzels sells for $1.80.
[U]Build the cost function C(b) where b is the number of bags of pretzels:[/U]
C(b) = Cost per bag * b + Fixed Costs
C(b) = 0.70b + 1100
[U]Build the revenue function R(b) where b is the number of bags of pretzels:[/U]
R(b) = Sale price * b
R(b) = 1.80b
[U]Build the revenue function P(b) where b is the number of bags of pretzels:[/U]
P(b) = Revenue - Cost
P(b) = R(b) - C(b)
P(b) = 1.80b - (0.70b + 1100)
P(b) = 1.80b = 0.70b - 1100
P(b) = 1.10b - 1100

A printer can print 25 pages per minute. At this rate, how long will it take to print 2000 pages?

A printer can print 25 pages per minute. At this rate, how long will it take to print 2000 pages?
Let m be the number of minutes it takes to print 2,000 pages. We have the equation:
25m = 2000
[URL='https://www.mathcelebrity.com/1unk.php?num=25m%3D2000&pl=Solve']Type this equation into our search engine[/URL], and we get:
m = 80

A printer prints 2 photos each minute. Let P be the number of photos printed in M minutes. Write an

A printer prints 2 photos each minute. Let P be the number of photos printed in M minutes. Write an equation relating P to M.
Set up the equation P(M).
[B]P(M) = 2M[/B]
Read this as for every minute that goes by, 2 photos are printed.

A private high school charges $36,400 for tuition, but this figure is expected to rise 10% per year.

A private high school charges $36,400 for tuition, but this figure is expected to rise 10% per year. What will tuition be in 10 years?
Let the tuition be T(y) where y is the number of years from now. We've got:
T(y) = 36400 * (1.1)^y
The problem asks for T(10)
T(10) = 36400 * (1.1)^10
T(10) = 36400 * 2.5937424601
T(10) = [B]94,412.23[/B]

A private high school charges $52,200 for tuition, but this figure is expected to rise 7% per year.

A private high school charges $52,200 for tuition, but this figure is expected to rise 7% per year. What will tuition be in 3 years?
We have the following appreciation equation A(y) where y is the number of years:
A(y) = Initial Balance * (1 + appreciation percentage)^ years
Appreciation percentage of 7% is written as 0.07, so we have:
A(3) = 52,200 * (1 + 0.07)^3
A(3) = 52,200 * (1.07)^3
A(3) = 52,200 * 1.225043
A(3) = [B]63,947.25[/B]

A problem states: "There are 9 more children than parents in a room. There are 25 people in the room

A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?"
Let the number of children be c. Let the number of parents be p
We're given:
[LIST=1]
[*]c = p + 9 [I](9 more children than parents)[/I]
[*]c + p = 25
[/LIST]
to solve this system of equations, we plug equation (1) into equation (2) for c:
(p + 9) + p = 25
Group like terms:
2p + 9 = 25
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=2p%2B9%3D25&pl=Solve']type it in our search engine[/URL] and we get:
p = [B]8[/B]

A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for

A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joe's phone bill was $60 under this promotional deal, how many minutes of phone calls did he make? Round to the nearest integer if necessary.
Let m be the number of minutes Joe used. We have a cost function of:
C(m) = 0.05m + 15
If C(m) = 60, then we have:
0.05m + 15 = 60
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05m%2B15%3D60&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = [B]900[/B]

A quarter of a number is greater than or equal to 38

A quarter of a number is greater than or equal to 38.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
A quarter of a number means 1/4, so we have:
x/4
The phrase [I]is greater than or equal to[/I] means an inequality, so we use the >= sign in relation to 38:
[B]x/4 >= 38 <-- This is our algebraic expression
[/B]
If you want to solve this inequality, [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=38&propsign=%3E%3D&den1=4&den2=1&pl=Calculate+missing+proportion+value']we type it in the search engine[/URL] to get:
x >= [B]152[/B]

A quarter of the learners in a class have blond hair and two thirds have brown hair. The rest of the

A quarter of the learners in a class have blond hair and two thirds have brown hair. The rest of the learners in the class have black hair. How many learners in the class if 9 of them have blonde hair?
Total learners = Blond + Brown + Black
Total Learners = 1/4 + 2/3 + Black
Total Learners will be 1, the sum of all fractions
1/4 + 2/3 + Black = 1
Using common denominators of 12, we have:
3/12 + 8/12 + Black = 12/12
11/12 + Black = 12/12
Subtract 11/12 from each side:
Black = 1/12
Let t be the total number of people in class. We are given for blondes:
1/4t = 9
Multiply each side by 4
[B]t = 36[/B]
Brown Hair
2/3(36) = 24
Black Hair
1/12(36) = 3

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leis

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.22 hours, with a standard deviation of 2.31 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.29 hours, with a standard deviation of 1.58 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children (u1 - u2)
What is the interpretation of this confidence interval?
A. There is 90% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours
B. There is a 90% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours
C. There is 90% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours
D. There is a 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours
0.2021 < u1 - u2 < 1.6579 using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+40&xbar1=+5.22&stdev1=2.31&n2=40&xbar2=4.29&stdev2=1.58&conf=+90&pl=Mean+Diff+Conf.+Interval+%28Large+Sample%29']difference of means confidence interval calculator[/URL]
[B]Choice D
There is a 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours[/B]

A random sample of STAT200 weekly study times in hours is as follows: 2 15 15 18 30 Find the sam

A random sample of STAT200 weekly study times in hours is as follows: 2 15 15 18 30 Find the sample standard deviation. (Round the answer to two decimal places. Show all work.)
[B]9.98[/B] using [URL='http://www.mathcelebrity.com/statbasic.php?num1=+2,15,15,18,30&num2=+0.2,0.4,0.6,0.8,0.9&pl=Number+Set+Basics']our standard deviation calculator[/URL]

A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you ge

A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you get 92. What is the number?
Let the rational number be x. We're given:
7x/3 - 3/2 = 92
Using a common denominator of 3*2 = 6, we rewrite this as:
14x/6 - 9/6 = 92
(14x - 9)/6 = 92
Cross multiply:
14x - 9 = 92 * 6
14x - 9 = 552
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=14x-9%3D552&pl=Solve']type this equation into our search engine [/URL]and we get:
x = [B]40.07[/B]

A recipe that makes 25 oatmeal cookies calls for 2.5 cups of oats and one cup of sugar. Jerry needs

A recipe that makes 25 oatmeal cookies calls for 2.5 cups of oats and one cup of sugar. Jerry needs to make 195 cookies for his school party. How many cups of oats will he need?
Set up a proportion of oats to cookies where c is the number of cups needed to make 195 cookies
2.5/25 = c/195
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=2.5&num2=c&den1=25&den2=195&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
c = [B]19.5[/B]

A recipie calls for 2 tablespoons of olive oil for every 3 servings. How much olive oil will be nee

A recipe calls for 2 tablespoons of olive oil for every 3 servings. How much olive oil will be needed for 6 servings?
Set up a proportion of tablespoons to servings:
2/3 = o/6 where o is the number of tablespoons per 6 servings.
[URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=o&den1=3&den2=6&propsign=%3D&pl=Calculate+missing+proportion+value']Type 2/3 = o/6 into our search engine[/URL], and we get [B]o = 4[/B].

A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation t

A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation to determine the break even point?
Set up the cost functions for Rental Truck 1 (R1) and Rental Truck 2 (R2) where m is the number of miles
R1(m) = 0.59m + 49.95
R2(m) = 0.99m + 39.95
Break even is when we set the cost functions equal to one another:
0.59m + 49.95 = 0.99m + 39.95
[URL='https://www.mathcelebrity.com/1unk.php?num=0.59m%2B49.95%3D0.99m%2B39.95&pl=Solve']Typing this equation into the search engine[/URL], we get [B]m = 25[/B].

A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour. Write an

A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour. Write and solve an equation to find the number of hours spent repairing the car.
Let h be the number of hours spent repairing the car. We set up the cost function C(h):
C(h) = Labor Cost per hour * h + Parts Cost
We're given C(h) = 648.85, parts cost = 265.95, and labor cost per hour of 85, so we have:
85h + 265.95 = 648.85
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=85h%2B265.95%3D648.85&pl=Solve']type this into our search engine[/URL] and we get:
h = [B]4.5[/B]

A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and s

A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and solve an equation to find the number of hours of labor spent repairing the car
Set up the cost equation C(h) where h is the number of labor hours:
C(h) = Labor Cost per hour * h + Parts Cost
We're given C(h) = 553, Parts Cost = 265, and Labor Cost per Hour = 48. So we plug these in:
48h + 265 = 553
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=48h%2B265%3D553&pl=Solve']type it in our math engine[/URL] and we get:
h = [B]6 hours[/B]

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will excee

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will exceed flood stage. How long can the river rise at this rate without exceeding flood stage?
Let the number of inches be i. Remember 12 inches to a foot, so we have 2 feet = 12*2 = 24 inches.
[LIST]
[*]Inequality: 3i <= 24. (since more than means the river can go [U]up to[/U] 2 feet or 24 inches
[/LIST]
To solve the inequality for I, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3i%3C%3D24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]I <= 8
This means after 8 hours, the river will flood[/B]

a roller coaster has 6 trains. each train has 3 cars, and each car seats 4 people. write and simplif

a roller coaster has 6 trains. each train has 3 cars, and each car seats 4 people. write and simplify an expression including units to find the total number of people that can ride the roller coaster at one time
6 trains * 3 cars per train * 4 people per car = [B]72 people[/B]

A salesperson drove 9 hours. How long will he have driven t hours later?

Set up a function where t is the number of hours driven, and f(t) is the distance driven after t hours:
[B]f(t) = 9t[/B]

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis?
Slope is y/x,so we have 27/36.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=27%2F36&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we can reduce 27/36 to 3/4. So this is our slope.
[B]3/4[/B]

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis?
Slope = Rise/Run or y/x
Since tests are on the y-axis and time is on the x-axis, we have:
Slope = 27/36
We can simplify this, so we [URL='https://www.mathcelebrity.com/fraction.php?frac1=27%2F36&frac2=3%2F8&pl=Simplify']type in 27/36 into our search engine[/URL], and get:
[B]Slope = 3/4[/B]

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 f

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 9 sophomores, 7 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen?
We want combinations for freshmen, sophomores, juniors, and seniors.
[LIST]
[*]Freshmen choices: [URL='https://www.mathcelebrity.com/permutation.php?num=6&den=2&pl=Combinations']6 C 2[/URL] = 15
[*]Sophomore choices: [URL='https://www.mathcelebrity.com/permutation.php?num=9&den=3&pl=Combinations']9 C 3[/URL] = 84
[*]Junior choices: [URL='https://www.mathcelebrity.com/permutation.php?num=7&den=4&pl=Combinations']7 C 4[/URL] = 35
[*]Senior choices: [URL='https://www.mathcelebrity.com/permutation.php?num=7&den=5&pl=Combinations']7 C 5 [/URL]= 21
[/LIST]
The number of committees we can choose is the product of combinations of freshmen, sophomores, juniors, and seniors.
Total Committees = Freshmen choices * Sophomore choices * Junior choices * Senior choices
Total Committees = 15 * 84 * 35 * 21
Total Committees = [B]926,100[/B]

A school spent $150 on advertising for a breakfast fundraiser. Each plate of food was sold for $8.00

A school spent $150 on advertising for a breakfast fundraiser. Each plate of food was sold for $8.00 but cost the school $2.00 to prepare. After all expenses were paid, the school raised $2,400 at the fundraiser. Which equation can be used to find x, the number of plates that were sold?
Set up the cost equation C(x) where x is the number of plates sold:
C(x) = Cost per plate * x plates
C(x) = 2x
Set up the revenue equation R(x) where x is the number of plates sold:
R(x) = Sales price per plate * x plates
C(x) = 8x
Set up the profit equation P(x) where x is the number of plates sold:
P(x) = R(x) - C(x)
P(x) = 8x - 2x
P(x) = 6x
We're told the profits P(x) for the fundraiser were $2,400, so we set 6x equal to 2400 and solve for x:
6x = 2400
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x%3D2400&pl=Solve']type it in our math engine[/URL] and we get:
x =[B]400 plates[/B]

A school theater group is selling candy to raise funds in order to put on their next performance. Th

A school theater group is selling candy to raise funds in order to put on their next performance. The candy cost the group $0.20 per piece. Plus, there was a $9 shipping and handling fee. The group is going to sell the candy for $0.50 per piece. How many pieces of candy must the group sell in order to break even?
[U]Set up the cost function C(p) where p is the number of pieces of candy.[/U]
C(p) = Cost per piece * p + shipping and handling fee
C(p) = 0.2p + 9
[U]Set up the Revenue function R(p) where p is the number of pieces of candy.[/U]
R(p) = Sale price * p
R(p) = 0.5p
Break-even means zero profit or loss, so we set the Cost Function equal to the Revenue Function
0.2p + 9 = 0.5p
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B9%3D0.5p&pl=Solve']type it in our math engine[/URL] and we get:
p = [B]30[/B]

A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number?

A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number?
Take this algebraic expression in pieces:
[LIST]
[*]Let the secret number be n.
[*]Added to means we add 6 to n: n + 6
[*]The total is multiplied by 5: 5(n + 6)
[*]The phrase [I]to get[/I] means equal to, so we set 5(n + 6) equal to 50
[/LIST]
5(n + 6) = 50
To solve this equation for n, we type it in our search engine and we get:
n = [B]4[/B]

A segment has an endpoint at (2, 1). The midpoint is at (5, 1). What are the coordinates of the othe

A segment has an endpoint at (2, 1). The midpoint is at (5, 1). What are the coordinates of the other endpoint?
The other endpoint is (8,1) using our [URL='http://www.mathcelebrity.com/mptnline.php?ept1=2&empt=5&ept2=&pl=Calculate+missing+Number+Line+item']midpoint calculator.[/URL]

A service charges a $1.95 flat rate plus $0.05 per mile . Jason only has $12 to spend on a a ride

A service charges a $1.95 flat rate plus $0.05 per mile. Jason only has $12 to spend on a a ride.
Set up the cost equation C(m) where m is the number of miles:
C(m) = 0.05m + 1.95
The problems asks for the number of miles (m) when C(m) = 12:
0.05m + 1.95 = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05m%2B1.95%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = [B]201[/B]

A set of 19 scores has a mean of 6.3. A new score of 8 is then included in the data set. What is th

A set of 19 scores has a mean of 6.3. A new score of 8 is then included in the data set. What is the new mean?
We know the mean formula is:
Sum of scores / Number of Scores = Mean
We're given mean = 6.3 and number of scores = 19, so we have:
Sum of scores / 19 = 6.3
Cross multiply:
Sum of scores = 19 * 6.3
Sum of scores = 119.7
Now a new score is added of 8, so we have:
Sum of scores = 119.7 + 8 = 127.7
Number of scores = 19 + 1 = 20
So our new mean is:
Mean = Sum of scores / Number of Scores
Mean = 127.7/20
Mean = [B]6.385[/B]
[COLOR=rgb(0, 0, 0)][SIZE=5][FONT=arial][B][/B][/FONT][/SIZE][/COLOR]

A sewing class has 205 yards off a bric to make quilts. Each quilt requires 7 yards off a bric. How

A sewing class has 205 yards off a bric to make quilts. Each quilt requires 7 yards off a bric. How much will remain after all the quilts are made?
Calculate the number of full quilts:
205/7 = 29.2857 so 29 full quilts.
29 * 7 = 203
205 - 203 = [B]2 yards remaining[/B].
You can also use the [URL='http://www.mathcelebrity.com/modulus.php?num=205mod7&pl=Calculate+Modulus']modulus calculator[/URL]

A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package

A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package weight. Write an equation to represent the price P of shipping a package that weighs x ounces, for any whole number of ounces greater than or equal to 1.
Set up the price function P(x)
[B]P(x) = 0.43 + 0.29(x - 1)[/B]

A shopkeeper buys a box of 20 cans of cola for $10. He sells the cans for 65 cents each. Work out hi

A shopkeeper buys a box of 20 cans of cola for $10. He sells the cans for 65 cents each. Work out his percentage profit.
[U]Calculate Revenue[/U]
Revenue = Sale price per can * number of cans
Revenue = 0.65 * 20
Revenue = 13
[U]Calculate Profit given a cost of $10:[/U]
Profit = Revenue - Cost
Profit = 13 - 10
Profit = 3
[U]Calculate Percentage Profit:[/U]
Percentage Profit = Profit/Revenue * 100%
Percentage Profit = 3/13 * 100%
Percentage Profit = 0.23076923076 * 100%
Percentage Profit = [B]23.08%[/B]

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $75. A seas

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $75. A season ski pass costs $350. The skier would have to rent skis with either pass for $20 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Let d be the number of days:
Daily Plan cost: 75d + 20d = 95d
Season Pass: 350 + 20d
We want to find d such that
350 + 20d < 95d
Subtract 20d from each side
75d > 350
Divide each side by 75
d > 4.66667
[B]d = 5[/B]

A soccer team is buying T-shirts to sell as a fundraiser. The team pays a flat fee of $35 for a logo

A soccer team is buying T-shirts to sell as a fundraiser. The team pays a flat fee of $35 for a logo design plus $7.00 per T-shirt.
Set up the cost function C(t) where t is the number of t-shirts:
C(t) = Cost per t-shirt * number of t-shirts + Flat Fee
[B]C(t) = 7t + 35[/B]

A social networking site currently has 38,000 active members per month, but that figure is dropping

A social networking site currently has 38,000 active members per month, but that figure is dropping by 5% with every month that passes. How many active members can the site expect to have in 7 months?
Setup an equation S(m) where m is the number of months that pass:
S(m) = 38000 * (1 - 0.05)^t
S(m) = 38000 * (0.95)^t
The problem asks for S(7):
S(7) = 38000 * (0.95)^7
S(7) = 38000 * (0.69833729609)
S(7) = 26,536.82
We round down to a full person and get:
S(7) = [B]26,536[/B]

A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 w

A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 white. The pointer is spun and a marble is picked at random.
a) Use a tree diagram to list the possible outcomes.
[LIST=1]
[*][B]A, Grey[/B]
[*][B]A, Black[/B]
[*][B]A, White[/B]
[*][B]B, Grey[/B]
[*][B]B, Black[/B]
[*][B]B, White[/B]
[*][B]C, Grey[/B]
[*][B]C, Black[/B]
[*][B]C, White[/B]
[/LIST]
b) What is the probability of:
i) spinning A?
P(A) = Number of A sections on spinner / Total Sections
P(A) = [B]1/3[/B]
---------------------------------
ii) picking a grey marble?
P(A) = Number of grey marbles / Total Marbles
P(A) = [B]1/3[/B]
---------------------------------
iii) spinning A and picking a white marble?
Since they're independent events, we multiply to get:
P(A AND White) = P(A) * P(White)
P(A) was found in i) as 1/3
Find P(White):
P(White) = Number of white marbles / Total Marbles
P(White) = 1/3
[B][/B]
Therefore, we have:
P(A AND White) = 1/3 * 1/3
P(A AND White) = [B]1/9[/B]
---------------------------------
iv) spinning C and picking a pink marble?
Since they're independent events, we multiply to get:
P(C AND Pink) = P(C) * P(Pink)
Find P(C):
P(C) = Number of C sections on spinner / Total Sections
P(C) = 1/3
[B][/B]
Find P(Pink):
P(Pink) = Number of pink marbles / Total Marbles
P(Pink) = 0/3
[B][/B]
Therefore, we have:
P(C AND Pink) = 1/3 * 0
P(C AND Pink) = [B]0[/B]

A spinner has 6 equal sections, of which 2 are green. If you spin the spinner once, what is the prob

A spinner has 6 equal sections, of which 2 are green. If you spin the spinner once, what is the probability that it will land on a green section? Write your answer as a fraction or whole number.
P(green) = Total Green / Total spaces
P(green) = 2/6
We can simplify this fraction. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F6&frac2=3%2F8&pl=Simplify']type 2/6 into our search engine[/URL], choose Simplify, and we get:
P(green) = [B]1/3[/B]

A spinner is divided into 4 equal sections numbered 1 to 4. The theoretical probability of the spinn

A spinner is divided into 4 equal sections numbered 1 to 4. The theoretical probability of the spinner stopping on 3 is 25%. Which of the following is most likely the number of 3s spun in 10,000 spins?
We want Expected Value of s spins. Set up the expected value formula for any number 1-4
E(s) = 0.25 * n where n is the number of spins.
Using s = 3, n = 10,000, we have:
E(10,000) = 0.25 * 10,000
E(10,000) = [B]2,500[/B]

A sports tournament has c teams. Each team has 17 players. Using c, write

A sports tournament has c teams. Each team has 17 players. Using c, write an expression for the total number of players in the tournament.
Total Players = Total Teams * Players Per Team
Total Players =[B] 17c[/B]

A sports tournament has d teams. Each team has 14 players. Using d, write an expression for the tota

A sports tournament has d teams. Each team has 14 players. Using d, write an expression for the total number of players in the tournament.
Tournament Players = Players per team * Number of Teams
Tournament Players = [B]14d[/B]

A standard die is rolled. Find the probability that the number rolled is greater than 3

A standard die is rolled. Find the probability that the number rolled is greater than 3.
Using our [URL='http://www.mathcelebrity.com/1dice.php?gl=2&pl=3&opdice=1&rolist=+2%2C3%2C4&dby=+2%2C3%2C5&montect=+100']dice calculator[/URL], the probability is [B]1/2 or 0.5[/B]

a stone mason builds 7 houses in 3 days. How many days does it take to build 11 houses?

a stone mason builds 7 houses in 3 days. How many days does it take to build 11 houses?
The build rate of houses per days is proportional. Set up a proportion of [I]houses to days[/I] where d is the number of days it takes to build 11 houses:
7/3 = 11/d
Cross multiply:
Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2
7d = 11 * 3
7d = 33
Divide each side of the equation by 7:
7d/7 = 33/7
d = [B]4.7142857142857[/B]

A store manager must calculate the total number of winter hats available to sell in the store from a

A store manager must calculate the total number of winter hats available to sell in the store from a starting number of 293. In the past month, the store sold 43 blue hats, 96 black hats, 28 red hats, and 61 pink hats. The store received a shipment of 48 blue hats, 60 black hats, 18 red hats, and 24 pink hats. How many total hats does the store have for sale?
[LIST=1]
[*]We start with 293 hats
[*]We calculate the hats sold: (43 + 96 + 28 + 61) = 228
[*]We subtract Step 2 from Step 1 to get remaining hats before the shipment: 293 - 228 = 65
[*]Now we calculate the number of hats received in the shipment: (48 + 60 + 18 + 24) = 150
[*]We add Step 4 to Step 3: 65 + 150 = [B]215 hats for sale[/B]
[/LIST]

a student has $50 in saving and earns $40 per week. How long would it take them to save $450

a student has $50 in saving and earns $40 per week. How long would it take them to save $450
Set up the savings function S(w), where w is the number of weeks. The balance, S(w) is:
S(w) = Savings Per week * w + Initial Savings
S(w) = 40w + 50
The problems asks for how many weeks for S(w) = 450. So we have;
40w + 50 = 450
To solve for w, we[URL='https://www.mathcelebrity.com/1unk.php?num=40w%2B50%3D450&pl=Solve'] type this equation in our search engine[/URL] and we get:
w = [B]10[/B]

A submarine dove 132.58 meters to reach a resting depth of 700 meter below sea level. What was it's

A submarine dove 132.58 meters to reach a resting depth of 700 meter below sea level. What was it's original depth
Below sea level is a negative amount. So they end up at -700.
To go back up toward sea level, we'd be at:
-700 + 132.58 = -567.42
Negative numbers mean below sea level, so the original depth was [B]567.42 meters below sea level[/B]

A submarine hovers at 240 meters below sea level. If it descends 160 meters and then ascends 390 met

A submarine hovers at 240 meters below sea level. If it descends 160 meters and then ascends 390 meters, what is its new position?
240 meters below sea level means a negative number, so we start with:
-240
Descending 160 meters means our depth decreases, so we subtract:
-240 - 160 = -400
Ascends means our depth increases, so we add:
-400 + 390 = [B]-10 or 10 feet below sea level[/B]

A submarine is 75 feet below sea level. It descends another 25 feet every 10 seconds for 3 minutes.

A submarine is 75 feet below sea level. It descends another 25 feet every 10 seconds for 3 minutes. What integer represents the submarines current location?
Assumptions and givens:
[LIST]
[*]Let m be the number of minutes
[*]10 seconds is 1/6 of a minute, 6 (10) seconds blocks per minute * 3 minutes = 18 (10 second blocks)
[*]Below sea level is a negative number
[/LIST]
[U]Current depth:[/U]
-25(18) - 75
-450 - 75
[B]-525[/B]

A suitcase contains nickels, dimes and quarters. There are 2&1/2 times as many dimes as nickels and

A suitcase contains nickels, dimes and quarters. There are 2&1/2 times as many dimes as nickels and 5 times the number of quarters as the number of nickels. If the coins have a value of $24.80, how many nickels are there in the suitcase?
Setup number of coins:
[LIST]
[*]Number of nickels = n
[*]Number of dimes = 2.5n
[*]Number of quarters = 5n
[/LIST]
Setup value of coins:
[LIST]
[*]Value of nickels = 0.05n
[*]Value of dimes = 2.5 * 0.1n = 0.25n
[*]Value of quarters = 5 * 0.25n = 1.25n
[/LIST]
Add them up:
0.05n + 0.25n + 1.25n = 24.80
Solve for [I]n[/I] in the equation 0.05n + 0.25n + 1.25n = 24.80
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(0.05 + 0.25 + 1.25)n = 1.55n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
1.55n = + 24.8
[SIZE=5][B]Step 3: Divide each side of the equation by 1.55[/B][/SIZE]
1.55n/1.55 = 24.80/1.55
n = [B]16[/B]
[B]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05n%2B0.25n%2B1.25n%3D24.80&pl=Solve']Source[/URL][/B]

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, t

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, there are 25 zombies. After how many days will there be over 25,000 zombies?
We set up our exponential function where n is the number of days after today:
Z(n) = 25 * 2^n
We want to know n where Z(n) = 25,000.
25 * 2^n = 25,000
Divide each side of the equation by 25, to isolate 2^n:
25 * 2^n / 25 = 25,000 / 25
The 25's cancel on the left side, so we have:
2^n = 1,000
Take the natural log of each side to isolate n:
Ln(2^n) = Ln(1000)
There exists a logarithmic identity which states: Ln(a^n) = n * Ln(a). In this case, a = 2, so we have:
n * Ln(2) = Ln(1,000)
0.69315n = 6.9077
[URL='https://www.mathcelebrity.com/1unk.php?num=0.69315n%3D6.9077&pl=Solve']Type this equation into our search engine[/URL], we get:
[B]n = 9.9657 days ~ 10 days[/B]

A survey of 950 college students found that 85% of the men and 90% of the women identified math as t

A survey of 950 college students found that 85% of the men and 90% of the women identified math as their favorite subject. If altogether 834 students reported math to be their favorite subject how many men and women participated in the survey
Let m be the number of men and w be the number of women. We are given 2 equations
[LIST=1]
[*]m + w = 950
[*]0.85m + 0.90w = 834
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+w+%3D+950&term2=0.85m+%2B+0.90w+%3D+834&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[LIST]
[*]m = [B]420[/B]
[*]w = [B]530[/B]
[/LIST]

A survey was conducted that asked 1007 people how many books they had read in the past year. Results

A survey was conducted that asked 1007 people how many books they had read in the past year. Results indicated that x overbarequals11.3 books and sequals16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval.
x bar = 11.3
s = 16.6
n = 1007
[URL='https://www.mathcelebrity.com/normconf.php?n=1007&xbar=11.3&stdev=16.6&conf=90&rdig=4&pl=Not+Sure']We use our confidence interval calculator[/URL] and get [B]10.4395 < u < 12.1605[/B].
[B][I]We interpret this as:
If we repeated experiments, the proportion of such intervals containing u would be 90%[/I][/B]

A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take

A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take for the tank to be empty
Assumptions and givens:
[LIST]
[*]Let the number of seconds be s.
[*]An empty tank means 0 liters of water.
[*]Leaks mean we subtract from the starting volume.
[/LIST]
We have the following relation:
800 - 12s = 0
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=800-12s%3D0&pl=Solve']type it in our search engine[/URL] and we get:
s = 66.67 seconds

A taxi cab in Chicago charges $3 per mile and $1 for every person. If the taxi cab ride for two peop

A taxi cab in Chicago charges $3 per mile and $1 for every person. If the taxi cab ride for two people costs $20. How far did the taxi cab travel.
Set up a cost function C(m) where m is the number of miles driven:
C(m) = cost per mile * m + per person fee
[U]Calculate per person fee:[/U]
per person fee = $1 per person * 2 people
per person fee = $2
[U]With a cost per mile of $3 and per person fee of $2, we have:[/U]
C(m) = cost per mile * m + per person fee
C(m) = 3m + 2
The problem asks for m when C(m) = 20, so we set 3m + 2 equal to 20:
3m + 2 = 20
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%2B2%3D20&pl=Solve']plug it in our search engine[/URL] and we get:
m = [B]6[/B]

A taxi cab in nyc charges a pick up fee of $5.00 . The customer must also pay $2.59 for each mile th

A taxi cab in nyc charges a pick up fee of $5.00 . The customer must also pay $2.59 for each mile that the taxi must drive to reach their destination. Write an equation
Set up a cost function C(m) where m is the number of miles:
C(m) = Mileage Charge * m + pick up fee
[B]C(m) = 2.59m + 5[/B]

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to s

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel?
Set up the travel cost equation where m is the number of miles:
C(m) = 0.8m + 1.50
If Samantha wants to spend less than 12 per ride, we have an inequality where C(m) < 12:
[B]0.8m + 1.50 < 12[/B]

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to s

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel?
[LIST]
[*]Each ride will cost 1.50 + 0.8x where x is the number of miles per trip.
[*]This expression must be less than 12.
[/LIST]
[U]Setup the inequality:[/U]
1.5 + 0.8x < 12
[U]Subtracting 1.5 from each side of the inequality[/U]
0.8x < 10.5
[U]Simplifying even more by dividing each side of the inequality by 0.8, we have:[/U]
[B]x < 13.125[/B]

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel?
Set up a cost function C(m), where m is the number of miles:
C(m) = Cost per mile * m + flat rate
C(m) = 0.65m + 1.75
The problem asks for m when C(m) = 10
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get:
m = [B]12.692 miles[/B]

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel
Set up a cost function C(m), where m is the number of miles Erica can travel. We have:
C(m) = 0.65m + 1.75
If C(m) = 10, we have:
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = 12.69 miles
If the problem asks for complete miles, we round down to 12 miles.

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel?
Set up the cost function C(m) where m is the number of miles:
C(m) = 0.65m + 1.75
If Erica has $10, then C(m) = 10, so we have:
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get
m = 12.69
if the answer asks for whole number, then we round down to m = 12

A taxi charges a flat rate of 1.75, plus an additional 0.65 per mile. If Erica has at most 10 to spe

A taxi charges a flat rate of 1.75, plus an additional 0.65 per mile. If Erica has at most 10 to spend on the cab ride, how far could she travel?
Setup an equation where x is the number of miles traveled:
0.65x + 1.75 = 10
Subtract 1.75 from each side:
0.65x = 8.25
Divide each side by 0.65
[B]x = 12.69 miles[/B]
If we do full miles, we round down to 12.

a teacher puts 1125 marbles into 9 containers to put the same number of marbles into each container

a teacher puts 1125 marbles into 9 containers to put the same number of marbles into each container how many marbles does the teacher put into each container
marbles per container = Total marbles / total containers
marbles per container = 1125/9
marbles per container = [B]125[/B]

A test has three true-false questions. Find the total number of ways you can answer the three questi

A test has three true-false questions. Find the total number of ways you can answer the three questions
We can either choose T or F. So we have:
Question 1: 2 choies
Question 2: 2 choices
Question 3: 2 choices
2 * 2 * 2 = [B]8 choices
[/B]
[LIST=1]
[*][B]TTT[/B]
[*][B]TTF[/B]
[*][B]TFT[/B]
[*][B]FTT[/B]
[*][B]FTF[/B]
[*][B]FFT[/B]
[*][B]TFF[/B]
[*][B]FFF[/B]
[/LIST]

A test has twenty questions worth 100 points total. the test consists of true/false questions worth

A test has twenty questions worth 100 points total. the test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many true/false questions are on the test?
Let m be the number of multiple choice questions and t be the number of true/false questions. We're given:
[LIST=1]
[*]m + t = 20
[*]11m + 3t = 100
[/LIST]
We can solve this system of equations 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the following answers:
[LIST]
[*][B]m = 5[/B]
[*][B]t = 15[/B]
[/LIST]
Check our work in equation 1:
5 + 15 ? 20
[I]20 = 20[/I]
Check our work in equation 2:
11(5) + 3(15) ? 100
55 + 45 ? 100
[I]100 = 100[/I]

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 poin

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
Let the number of true/false questions be t. Let the number of multiple choice questions be m. We're given two equations:
[LIST=1]
[*]m + t = 20
[*]11m + 3t = 100
[/LIST]
We have a set of simultaneous equations. We can solve this using 3 methods:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we pick, we get the same answer:
[LIST]
[*][B]m = 5[/B]
[*][B]t = 15[/B]
[/LIST]

A text message plan costs $7 per month plus $0.28 per text. Find the monthly cost for x text message

A text message plan costs $7 per month plus $0.28 per text. Find the monthly cost for x text messages.
We set up the cost function C(x) where x is the number of text messages per month:
C(x) = Cost per text * x + Monthly cost
Plugging in our given numbers, we get:
[B]C(x) = 0.28x + 7[/B]

a textbook store sold a combined total of 296 sociology and history text books in a week. the number

a textbook store sold a combined total of 296 sociology and history text books in a week. the number of history textbooks sold was 42 less than the number of sociology textbooks sold. how many text books of each type were sold?
Let h = history book and s = sociology books. We have 2 equations:
(1) h = s - 42
(2) h + s = 296
Substitute (1) to (2)
s - 42 + s = 296
Combine variables
2s - 42 = 296
Add 42 to each side
2s = 338
Divide each side by 2
s = 169
So h = 169 - 42 = 127

A textbook store sold a combined total of 307 biology and chemistry textbooks in a week. The number

A textbook store sold a combined total of 307 biology and chemistry textbooks in a week. The number of chemistry textbooks sold was 71 less than the number of biology textbooks sold. How many textbooks of each type were sold?
Let b be the number of biology books and c be the number of chemistry books. We have two equations:
[LIST=1]
[*]b + c = 307
[*]c = b - 71
[/LIST]
Substitute (2) into (1) for c
b + (b - 71) = 307
Combine like terms:
2b - 71 = 307
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2b-71%3D307&pl=Solve']equation solver[/URL], we get:
[B]b = 189[/B]
Now substitute that into (2):
c = 189 - 71
[B]c = 118[/B]

A theater has 1200 seats. Each row has 20 seats. Write and solve an equation to find the number x of

A theater has 1200 seats. Each row has 20 seats. Write and solve an equation to find the number x of rows in the theater.
Let x be the number of rows in the theater:
x = Total Seats / Seats per row
x = 1200/20
x = [B]60[/B]

A theatre contains 459 seats and the ticket prices for a recent play were $53 for adults and $16 for

A theatre contains 459 seats and the ticket prices for a recent play were $53 for adults and $16 for children. If the total proceeds were $13,930 for a sold- out matinee, how many of each type of ticket were sold?
Let a be the number of adult tickets and c be the number of children tickets. We have the following equations:
[LIST=1]
[*]a + c =459
[*]53a + 16c = 13930
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a%2Bc%3D459&term2=53a+%2B+16c+%3D+13930&pl=Cramers+Method']simultaneous equation calculator[/URL], we have:
[B]a = 178
c = 281[/B]

A third of a pizza is 400 calories. How many calories in the whole pizza?

A third of a pizza is 400 calories. How many calories in the whole pizza?
Let c be the number of calories in the whole pizza. WE have:
c/3 = 400
To solve this proportion for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=c&num2=400&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and get:
c = [B]1,200[/B]

A three digit number, if the digits are unique

A three digit number, if the digits are unique
[LIST=1]
[*]For our first digit, we can start with anything but 0. So we have 9 options
[*]For our second digit, we can use anything but 9 since we want to be unique. So we have 9 options
[*]For our last digit, we can use anything but the first and second digit. So we have 10 - 2 = 8 options
[/LIST]
Our total 3 digit numbers with all digits unique is found by the fundamental rule of counting:
9 * 9 * 8 = [B]648 possible 3 digit numbers[/B]

A toffee jar contains 225 toffees . How many toffees will be there in 62 such toffee jars ?

A toffee jar contains 225 toffees . How many toffees will be there in 62 such toffee jars ?
Total Toffees = Toffee per jar * number of jars
Total Toffees = 225 * 62
Total Toffees = [B]13,950 toffees[/B]

A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was

A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was Marcos car towed if he received a bill for $71
Set up a cost equation C(m) where m is the number of miles:
C(m) = Cost per mile * m + Service Fee
Plugging in the service fee of 50 and cost per mile of 1.75, we get:
C(m) = 1.75m + 50
The question asks for what m is C(m) = 71. So we set C(m) = 71 and solve for m:
1.75m + 50 = 71
Solve for [I]m[/I] in the equation 1.75m + 50 = 71
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 50 and 71. To do that, we subtract 50 from both sides
1.75m + 50 - 50 = 71 - 50
[SIZE=5][B]Step 2: Cancel 50 on the left side:[/B][/SIZE]
1.75m = 21
[SIZE=5][B]Step 3: Divide each side of the equation by 1.75[/B][/SIZE]
1.75m/1.75 = 21/1.75
m = [B]12[/B]

A town has a population of 12000 and grows at 5% every year. What will be the population after 12 ye

A town has a population of 12000 and grows at 5% every year. What will be the population after 12 years, to the nearest whole number?
We calculate the population of the town as P(t) where t is the time in years since now.
P(t) = 12000(1.05)^t
The problem asks for P(12)
P(12) = 12000(1.05)^12
P(12) = 12000(1.79585632602)
P(12) = [B]21550[/B] <- nearest whole number

A towns population is currently 500. If the population doubles every 30 years, what will the populat

A towns population is currently 500. If the population doubles every 30 years, what will the population be 120 years from now?
Find the number of doubling times:
120 years / 30 years per doubling = 4 doubling times
Set up our growth function P(n) where n is the number of doubling times:
P(n) = 500 * 2^n
Since we have 4 doubling times, we want P(4):
P(4) = 500 * 2^4
P(4) = 500 * 16
P(4) = [B]8,000[/B]

A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. T

A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. The company sells each bear for $12.00 each. How many bears must this company sell in order to break even?
[U]Set up the cost function C(b) where b is the number of bears:[/U]
C(b) = Cost per bear * b + factory expenses
C(b) = 8b + 1500
[U]Set up the revenue function R(b) where b is the number of bears:[/U]
R(b) = Sale Price per bear * b
R(b) = 12b
[U]Break-even is where cost equals revenue, so we set C(b) equal to R(b) and solve for b:[/U]
C(b) = R(b)
8b + 1500 = 12b
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B1500%3D12b&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]375[/B]

A train ticket is 8 centimeters tall and 10 centimeters long. What is its area?

A train ticket is 8 centimeters tall and 10 centimeters long. What is its area?
The ticket is a rectangle. The area is:
A = lw
Plugging in our numbers, we get:
A = (8)(10)
A = 80

A tree grows 35 cm in 2 years. If it continues to grow at the same rate determine how long it would

A tree grows 35 cm in 2 years. If it continues to grow at the same rate determine how long it would take to grow 85 cm
We set up a proportion of cm to years where y is the number of years it takes to grow 85 cm:
35/2 = 85/y
To solve this proportion for y, [URL='https://www.mathcelebrity.com/prop.php?num1=35&num2=85&den1=2&den2=y&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
[B]y = 4.86[/B]

A triangular garden has base of 6 meters amd height of 8 meters. Find its area

A triangular garden has base of 6 meters amd height of 8 meters. Find its area
Area (A) of a triangle is:
A = bh/2
Plugging in our numbers, we get:
A = 6*8/2
A = [B]24 square meters[/B]

A used book store also started selling used CDs and videos. In the first week, the store sold a comb

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold
Let c be the number of CDs sold, and v be the number of videos sold. We're given 2 equations:
[LIST=1]
[*]c + v = 40
[*]4c + 6v = 180
[/LIST]
You can solve this system of equations three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter what method we choose, we get [B]c = 30, v = 10[/B].
Now let's check our work for both given equations for c = 30 and v = 10:
[LIST=1]
[*]30 + 10 = 40 <-- This checks out
[*]4c + 6v = 180 --> 4(30) + 6(10) --> 120 + 60 = 180 <-- This checks out
[/LIST]

A used book store also started selling used CDs and videos. In the first week, the store sold a comb

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold.
Let the number of cd's be c and number of videos be v. We're given two equations:
[LIST=1]
[*]c + v = 40
[*]4c + 6v = 180
[/LIST]
We can solve this system of equations using 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[B]c = 30
v = 10[/B]

A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $

A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company?
Set up a cost function C(m) where m is the number of movies you rent:
C(m) = Rental cost per movie * m + Membership Fee
[U]Video Store 1 cost function[/U]
C(m) = 1m + 7.5
Video Store 2 cost function:
C(m) = 2.50m
We want to know when the costs are the same. So we set each C(m) equal to each other:
m + 7.5 = 2.50m
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B7.5%3D2.50m&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]5[/B]

A virus is spreading exponentially. The initial amount of people infected is 40 and is increasing at

A virus is spreading exponentially. The initial amount of people infected is 40 and is increasing at a rate of 5% per day. How many people will be infected with the virus after 12 days?
We have an exponential growth equation below V(d) where d is the amount of days, g is the growth percentage, and V(0) is the initial infected people:
V(d) = V(0) * (1 + g/100)^d
Plugging in our numbers, we get:
V(12) = 40 * (1 + 5/100)^12
V(12) = 40 * 1.05^12
V(12) = 40 * 1.79585632602
V(12) = 71.8342530409 or [B]71[/B]

A water tank holds 236 gallons but is leaking at a rate of 3 gallons per week. A second water tank h

A water tank holds 236 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds 354 gallons but is leaking at a rate if 5 gallons per week. After how many weeks will the amount of water in the two tanks be the same
Let w be the number of weeks of leaking. We're given two Leak equations L(w):
[LIST=1]
[*]L(w) = 236 - 3w
[*]L(w) = 354 - 5w
[/LIST]
When the water in both tanks is the same, we can set both L(w) equations equal to each other:
236 - 3w = 354 - 5w
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=236-3w%3D354-5w&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]59[/B]

a well driller charges $9.00 per foot for the first 10 feet, 9.10 per foot for the next 10 feet, $9.

a well driller charges $9.00 per foot for the first 10 feet, 9.10 per foot for the next 10 feet, $9.20 per foot for the next 10 feet, and so on, at a price increase of $0.10 per foot for succeeding intervals of 10 feet. How much does it cost to drill a well to a depth of 150 feet?
Set up the cost function C(f) where f is the number of feet:
Cost = 9(10) + 9.1(10) + 9.2(10) + 9.3(10) + 9.4(10) + 9.5(10) + 9.6(10) + 9.7(10) + 9.8(10) + 9.9(10) + 10(10) + 10.1(10) + 10.2(10) + 10.3(10) + 10.4(10)
Cost = [B]1,455[/B]

a writer can write a novel at a rate of 3 pages per 5 hour work. if he wants to finish the novel in

a writer can write a novel at a rate of 3 pages per 5 hour work. if he wants to finish the novel in x number of pages, determine a function model that will represent the accumulated writing hours to finish his novel
if 3 pages = 5 hours, then we divide each side by 3 to get:
1 page = 5/3 hours per page
So x pages takes:
5x/3 hours
Our function for number of pages x is:
[B]f(x) = 5x/3[/B]

A zoo has 15 Emperor penguins. The Emperor penguins make up 30% percent of all the penguins at the z

A zoo has 15 Emperor penguins. The Emperor penguins make up 30% percent of all the penguins at the zoo. How many penguins live at the zoo?
Let p be the total number penguins at the zoo.
We're told:
30% of p = 15
Since 30% = 0.3, we have:
0.3p = 15
Solve for [I]p[/I] in the equation 0.3p = 15
[SIZE=5][B]Step 1: Divide each side of the equation by 0.3[/B][/SIZE]
0.3p/0.3 = 15/0.3
p = [B]50[/B]

a ^5 x a ^2 without exponents

a ^5 x a ^2 without exponents
When we multiply the same variable or number, we add exponents, so we have:
a^(5 + 2)
a^7
To write a variable raised to an exponent without exponents, we break it up. The formula to do this is:
a^n = a times itself n times
a^7 = [B]a * a * a * a * a * a * a[/B]

Aaron bought a bagel and 3 muffins for $7.25. Bea bought a bagel and 2 muffins for $6. How much is b

Aaron bought a bagel and 3 muffins for $7.25. Bea bought a bagel and 2 muffins for $6. How much is bagel and how much is a muffin?
Let b be the number of bagels and m be the number of muffins. We have two equations:
[LIST=1]
[*]b + 3m = 7.25
[*]b + 2m = 6
[/LIST]
Subtract (2) from (1)
[B]m = 1.25
[/B]
Plug this into (2), we have:
b + 2(1.25) = 6
b + 2.5 = 6
Subtract 2.5 from each side
[B]b = 3.5[/B]

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applie

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying [I]x[/I] nights?
[LIST]
[*]The Room cost equals 99.95 times x where x is the number of rooms
[*]We express an 8% tax by multiplying the room cost by 1.08
[*]Finally, we add on $5, which is [I]untaxed[/I]
[/LIST]
[I][/I]
Take this in pieces:
Room Cost: 99.95x
Tax on Room 1.08(99.95x)
Add on $5 which is untaxed: [B]1.08(99.95x) + 5[/B]

Abbey knew that the combination for her locker had the numbers 36, 12, 8, and 40, but she couldn't r

Abbey knew that the combination for her locker had the numbers 36, 12, 8, and 40, but she couldn't remember the right order of the numbers. How many different possibilities are there for the lock combination using the four numbers?
First number could be 4 choices, then 3, then 2, then 1. So we have:
4! = 4 x 3 x 2 x 1 = [B]24 possibilities[/B]

About 3/5th of the registered voters participated in 2016 election. California has 25 million regist

About 3/5th of the registered voters participated in 2016 election. California has 25 million registered voters. Find the number of registered voters who participated in 2016 election.
3[URL='https://www.mathcelebrity.com/fraction.php?frac1=25000000&frac2=3/5&pl=Multiply']/5 of 25000000[/URL] = [B]15,000,000[/B]

Absolute Difference

Calculates the absolute difference between 2 numbers

Absolute Value

Add, subtract, multiply or divide any two numbers with absolute value signs. Positive Difference.

Absolute value of x less than 8

These are now available as shortcuts. You can type any number or variable in the following forms:
[LIST]
[*]Absolute value of x less than 8
[*]Absolute value of x less than or equal to 8
[*]Absolute value of x greater than 8
[*]Absolute value of x greater than or equal to 8
[*]Absolute value of x equal to 8
[/LIST]

According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eatin

According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24. Over your lifetime, how many years will you spend on each of these activities?
Assumptions:
[LIST]
[*]Let years eating be e
[*]Let years sleeping be s
[/LIST]
We're given:
[LIST=1]
[*]s = e + 24
[*]e + s = 32
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for s:
e + e + 24 = 32
To solve this equation for e, we [URL='https://www.mathcelebrity.com/1unk.php?num=e%2Be%2B24%3D32&pl=Solve']type it in our math engine[/URL] and we get:
e = [B]4
[/B]
Now, we take e = 4 and substitute it into equation (1) to solve for s:
s = 4 + 24
s = [B]28[/B]

Add 5 to p, then divide the sum by 4

Add 5 to p, then divide the sum by 4
Add 5 to p:
p + 5
Divide the sum by 4:
[B](p + 5)/4
[/B]
note: B[I]ecause this is a sum, we wrap it in parentheses to divide the sum by a number[/I]

Add all the whole numbers 1 through 100

Add all the whole numbers 1 through 100
[URL='https://www.mathcelebrity.com/inclusnumwp.php?num1=1&num2=100&pl=Sum']Using our inclusive number word problem calculator[/URL], we get:
5,050

Addition and Multiplication Tables (Times Tables)

Shows the color coded addition or multiplication table entries and answer for any 2 numbers 1-15.

Addition of 3 or more numbers

This calculator performs addition with carrying and an addition grid for 3 or more numbers.

Additive Inverse Property

Demonstrates the Additive Inverse property using a number. A + (-A) = 0
Numerical Properties

Admission to a baseball game is $2.00 for general admission and $5.50 for reserved seats. The recei

Admission to a baseball game is $2.00 for general admission and $5.50 for reserved seats. The receipts were $3577.00 for 1197 paid admissions. How many of each ticket were sold?
Let g be the number of tickets for general admission
Let r be the number of tickets for reserved seats
We have two equations:
[LIST=1]
[*]g + r = 1197
[*]2g + 5.50r = 3577
[/LIST]
We can solve this a few ways, but let's use substitution using our [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=g+%2B+r+%3D+1197&term2=2g+%2B+5.50r+%3D+3577&pl=Substitution']simultaneous equations calculator[/URL]:
[LIST]
[*][B]r = 338[/B]
[*][B]g = 859[/B]
[/LIST]

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were col

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were collected for a total of 10,078.75, how many students attended the fair
Let the number of students be s and the others be o. We're given two equations:
[LIST=1]
[*]o + s = 2848
[*]3.75o + 2.50s = 10078.75
[/LIST]
Since we have no coefficients for equation 1, let's solve this the fast way using substitution. Rearrange equation 1 by subtracting o from each side to isolate s
[LIST=1]
[*]o = 2848 - s
[*]3.75o + 2.50s = 10078.75
[/LIST]
Now substitute equation 1 into equation 2:
3.75(2848 - s) + 2.50s =10078.75
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3.75%282848-s%29%2B2.50s%3D10078.75&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]481[/B]

After 5 years, a car is worth $22,000. It’s value decreases by $1,500 a year, which of the following

After 5 years, a car is worth $22,000. It’s value decreases by $1,500 a year, which of the following equations could represent this situation? Group of answer choices
Let y be the number of years since 5 years. Our Book value B(y) is:
[B]B(y) = 22,000 - 1500y[/B]

Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total v

Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total value of $3.50. How many of each type of coin does Ahmad have?
Let the number of 5-cent coins be f.
Let the number of 20-cent coins be t.
We're given two equations:
[LIST=1]
[*]f + t = 31
[*]0.05f + 0.2t = 3.50
[/LIST]
We can solve this simultaneous system of equations 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[LIST]
[*][B]f = 18[/B]
[*][B]t = 13[/B]
[/LIST]

Al's Rentals charges $25 per hour to rent a sailboard and a wetsuit. Wendy's Rentals charges $20 per

Al's Rentals charges $25 per hour to rent a sailboard and a wetsuit. Wendy's Rentals charges $20 per hour plus $15 extra for a wetsuit. Find the number of hours for which the total charges for both companies would be the same.
Al's Rentals Cost Equation C(h) where h is the number of hours you rent a sailboard and wetsuit:
C(h) = 25h
Wendy's Rentals Cost Equation C(h) where h is the number of hours you rent a sailboard and wetsuit:
C(h) = 20h + 15
We want to set both cost equation equal to each other, and solve for h:
20h + 15 = 25h
[URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B15%3D25h&pl=Solve']Typing this equation into our search engine[/URL], we get:
h = [B]3[/B]

Alec had c caramels. Then, Alecs sister took 85 of the caramels. Choose the expression that shows th

Alec had c caramels. Then, Alecs sister took 85 of the caramels. Choose the expression that shows the number of caramels Alec has left.
Alec starts with c caramels. His sister took 85. The word [I]took[/I] means subtract, so we have:
[B]c - 85[/B]

Algebraic Expressions

This calculator builds algebraic expressions based on word representations of numbers using the four operators and the words that represent them(increased,product,decreased,divided,times)
Also known as Mathematical phrases

algexpress: letthefirstnumberequalx.thesecondnumberis3morethantwicethefirstnumber.expressthesecondnu

Let the first number equal x. The second number is 3 more than twice the first number. Express the second number in terms of the first number x.
[LIST]
[*]Let the second number be y.
[*]Twice means multiply by 2
[*]3 more than means we add 3
[/LIST]
So we have the following algebraic expression:
[B]y = 2x + 3[/B]

Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of

Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today?
Let m be the number of minutes. The phrase [I]at least[/I] means an inequality, also known as greater than or equal to. So we have:
m >= 11*6
[B]m >= 66
You can read this as Ali will run 66 or more minutes today. Or at least 66 minutes. Or greater than or equal to 66 minutes[/B]

Aliyah had $24 to spend on seven pencils after buying them she had $10 how much did each pencil cost

Aliyah had $24 to spend on seven pencils after buying them she had $10 how much did each pencil cost?
If Aliyah had $24 to spend, and $10 left over, then she spent $24 - $10 = $14 on pencils
Find the cost per pencil:
Cost per pencil = Pencil Spend / Number of Pencils
Cost per pencil = 14/7
Cost per pencil = [B]$2[/B]

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil co

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?
Let p be the number of pencils. We're given the following equation:
7p + 10 = 24
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B10%3D24&pl=Solve']type it in our math engine[/URL] and we get:
p = [B]2
[/B]

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil co

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?
Let the number of pencils be p. We have:
7p + 10 = 24
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B10%3D24&pl=Solve']type it in our math engine[/URL] and we get:
p = [B]2[/B]

All real numbers that are less than equal to -1 or greater than 5

We have two expressions here, so we need a union since we have the word [U]or[/U].
First, All real numbers less than or equal to -1 is x <= -1.
All real numbers greater than 5 is x > 5
So we have x <= -1 U x > 5

all real numbers y greater than or equal to 12

all real numbers y greater than or equal to 12
Greater than or equal to means we use the sign >=
[B]y >= 12[/B]

Alonzo runs each lap in 4 minutes. He will run at most 32 minutes today. What are the possible numbe

Alonzo runs each lap in 4 minutes. He will run at most 32 minutes today. What are the possible numbers of laps he will run today?
32 minutes / 4 minutes per lap =[B] 8 laps maximum[/B]. He can also run less than 8 laps if his lap time gets slower.

Alorah joins a fitness center. She pays for a year plus a joining fee of $35. If the cost for the en

Alorah joins a fitness center. She pays for a year plus a joining fee of $35. If the cost for the entire year is $299, how much will she pay each month?
We set up the cost function C(m) where m is the number of months of membership:
C(m) = cost per month * m + joining fee
Plugging in our numbers from the problem with 12 months in a year, we get:
12c + 35 = 299
To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=12c%2B35%3D299&pl=Solve']type it in our search engine [/URL]and we get:
c = [B]22[/B]

Alya loves to read. She reads 90 pages in half an hour. How many pages does she read per minute?

Alya loves to read. She reads 90 pages in half an hour. How many pages does she read per minute?
Set up a proportion of pages to minutes. Since 30 minutes is a half hour, we have the number of pages (p) for 1 minute as:
90/30 = p/1
To solve this proportion for p, [URL='https://www.mathcelebrity.com/prop.php?num1=90&num2=p&den1=30&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
p = [B]3[/B]

Amanda runs each lap in 4 minutes. She will run less than 44 minutes today. What are the possible nu

Amanda runs each lap in 4 minutes. She will run less than 44 minutes today. What are the possible number of laps she will run today?
Notes for this problem:
[LIST]
[*]Let laps be l.
[*]Lap time = Time per lap * number of laps (l)
[*]Less than means we have an inequality using the < sign
[/LIST]
We have the inequality:
4l < 44
To solve this inequality for l, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4l%3C44&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get:
[B]l < 11[/B]

Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for ea

Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
Let the number of tv's be t. Set up the salary function S(t):
S(t) = Commision * tv's sold + Salary
Company A:
S(t) = 100t + 17,000
Company B:
S(t) = 20t + 29,000
The problem asks for how many tv's it takes to make both company salaries equal. So we set the S(t) functions equal to each other:
100t + 17000 = 20t + 29000
[URL='https://www.mathcelebrity.com/1unk.php?num=100t%2B17000%3D20t%2B29000&pl=Solve']Type this equation into our search engine[/URL] and we get:
t = [B]150[/B]

Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and in

Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and inside. Amy charges 40$ and Ryan charges 50$ . In addition they charge a hourly rate. Amy charges $35/h and ryan charges $30/h. How many hours does amy and ryan have to work to make the same amount of money?
Set up the cost functions C(h) where h is the number of hours.
[U]Amy:[/U]
C(h) = 35h + 40
[U]Ryan:[/U]
C(h) = 30h + 50
To make the same amount of money, we set both C(h) functions equal to each other:
35h + 40 = 30h + 50
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=35h%2B40%3D30h%2B50&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]2[/B]

Amy has n decks of cards. Each deck has 52 cards in it. Using n, write an expression for the total

Amy has n decks of cards. Each deck has 52 cards in it. Using n, write an expression for the total number of cards Amy has.
[B]52n[/B]

An airplane carries 500 passengers 45% are men, 20% are children. The number of women in the airplan

An airplane carries 500 passengers 45% are men, 20% are children. The number of women in the airplane is
If we assume the sample space is either men, women, or children to get 100% of the passengers, we have:
PercentWomen = 100% - Men - Children
PercentWomen = 100% - 45% - 20%
PercentWomen = 35%
Calculate Women passengers
Women passengers = Total passengers * Percent Women
Women passengers = 500 * 35%
Women passengers = [B]175[/B]

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 18

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 1800 feet per minute. Let m be the number of minutes. Which of the following expressions describe the height of the airplane after any given number of minutes?
Let m be the number of minutes. Since a descent equals a [U]drop[/U] in altitude, we subtract this in our Altitude function A(m):
[B]A(m) = 38,800 - 1800m[/B]

An auto repair bill is $126 for parts and $35 for each hour of labor. If h is the number of hours of

An auto repair bill is $126 for parts and $35 for each hour of labor. If h is the number of hours of labor, express the amount of the repair bill in terms of number of hours of labor.
Set up cost function, where h is the number of hours of labor:
[B]C(h) = 35h + 136[/B]

An auto repair bill was $563. This includes $188 for parts and $75 for each hour of labor. Find the

An auto repair bill was $563. This includes $188 for parts and $75 for each hour of labor. Find the number of hours of labor
Let the number of hours of labor be h. We have the cost function C(h):
C(h) = Hourly Labor Rate * h + parts
Given 188 for parts, 75 for hourly labor rate, and 563 for C(h), we have:
75h + 188 = 563
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=75h%2B188%3D563&pl=Solve']type it in our search engine[/URL] and we get:
h = [B]5[/B]

An eccentric millionaire has 5 golden hooks from which to hang her expensive artwork. She wants to h

An eccentric millionaire has 5 golden hooks from which to hang her expensive artwork. She wants to have enough paintings so she can change the order of the arrangement each day for the next 41 years. (The same five paintings are okay as long as the hanging order is different.) What is the fewest number of paintings she can buy and still have a different arrangement every day for the next 41 years?
365 days * 41 years + 10 leap year days = 14,975 days
what is the lowest permutations count of n such that nP5 >= 14,975
W[URL='https://www.mathcelebrity.com/permutation.php?num=9&den=5&pl=Permutations']e see that 9P5[/URL] = 15,120, so the answer is [B]9 paintings[/B]

An elevator can hold less than 2700 pounds of extra weight. If an average person weighs 150 pounds,

An elevator can hold less than 2700 pounds of extra weight. If an average person weighs 150 pounds, what is the maximum number of people (p) that can be on the elevator at one time?
Total weight = average weight per person * Number of people
Total weight = 150p
We know from the problem that:
150p < 2700
We want to solve this inequality for p. Divide each side of the inequality by 150:
150p/150 < 2700/150
Cancel the 150's on the left side and we get:
p < [B]18[/B]

An elevator can safely lift at most 4400 1bs. A concrete block has an average weight of 41 lbs. What

An elevator can safely lift at most 4400 1bs. A concrete block has an average weight of 41 lbs. What is the maximum number of concrete blocks that the elevator can lift?
Total blocks liftable = Lift Max / Weight per block
Total blocks liftable = 4400 / 41
Total blocks liftable = 107.31
We round down to whole blocks and we get [B]107[/B]

An elevator has a maximum weight of 3000 pounds. How many 150-pound people can safely ride the eleva

An elevator has a maximum weight of 3000 pounds. How many 150-pound people can safely ride the elevator? (Use "p" to represent the number of people)
Maximum means less than or equal to. We have the inequality:
150p <= 3000
To solve this inequality for p, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=150p%3C%3D3000&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]p <= 20[/B]

An estate has 6 houses and each house has x lighting fittings which need 1 lamp each, and y fittings

An estate has 6 houses and each house has x lighting fittings which need 1 lamp each, and y fittings which need 3 lamps each. Write a formula to find z, the total number of lamps needed on the estate.
z = 6(x * 1 + 3 * y)
z = [B]6(x + 3y)[/B]

An interior designer charges $100 to visit a site, plus $55 to design each room. Identify a function

An interior designer charges $100 to visit a site, plus $55 to design each room. Identify a function that represents the total amount he charges for designing a certain number of rooms. What is the value of the function for an input of 6, and what does it represent?
[U]Set up the cost function C(r) where r is the number of room to design:[/U]
C(r) = Cost per room * r + Site Visit Fee
C(r) = 55r + 100
[U]Now, the problem asks for an input of 6, which is [I]the number of rooms[/I]. So we want C(6) which is the [I]cost to design 6 rooms[/I]:[/U]
C(6) = 55(6) + 100
C(6) = 330 + 100
C(6) = [B]430[/B]

An international long distance phone call costs $0.79 per minute. How much will a 22 minute call cos

An international long distance phone call costs $0.79 per minute. How much will a 22 minute call cost?
[U]Calculate total cost:[/U]
Total cost = Cost per minute * number of minutes
Total cost = $0.79 * 22
Total cost = [B]$17.38[/B]

An orchard has 378 orange trees. The number of rows exceeds the number of trees per row by 3. How ma

An orchard has 378 orange trees. The number of rows exceeds the number of trees per row by 3. How many trees are there in each row?
We have r rows and t trees per row. We're give two equations:
[LIST=1]
[*]rt = 378
[*]r = t + 3
[/LIST]
Substitute equation (2) into equation (1) for r:
(t + 3)t = 378
Multiply through:
t^2 + 3t = 378
We have a quadratic equation. To solve this equation, we [URL='https://www.mathcelebrity.com/quadratic.php?num=t%5E2%2B3t%3D378&pl=Solve+Quadratic+Equation&hintnum=+0']type it in our search engine [/URL]and we get:
t = 18 and t = -21
Since t cannot be negative, we get trees per row (t):
[B]t = 18[/B]

An orchard has 816 apple trees. The number of rows exceeds the number of trees per row by 10. How ma

An orchard has 816 apple trees. The number of rows exceeds the number of trees per row by 10. How many trees are there in each row?
Let the rows be r and the trees per row be t. We're given two equations:
[LIST=1]
[*]rt = 816
[*]r = t + 10
[/LIST]
Substitute equation (2) into equation (1) for r:
(t + 10)t = 816
t^2 + 10t = 816
Subtract 816 from each side of the equation:
t^2 + 10t - 816 = 816 - 816
t^2 + 10t - 816 = 0
We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=t%5E2%2B10t-816%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type it in our search engine [/URL]and we get:
t = (24, -34)
Since the number of trees per row can't be negative, we choose [B]24[/B] as our answer

Ana has 24 carrots, 12 cucumbers, and 36 radishes. She wants to make identical vegetable baskets usi

Ana has 24 carrots, 12 cucumbers, and 36 radishes. She wants to make identical vegetable baskets using all of the vegetables. What is the greatest number of baskets she can make
The key to solving this problem is asking what is the common factor between the 3 numbers. We want the greatest common factor or GCF
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=12&num2=24&num3=36&pl=GCF']GCF(12, 24, 36) [/URL]= [B]12[/B]
We divide up our 12 baskets into carrots, cucumbers, and radishes. Each basket of the 12 baskets has the following:
[LIST=1]
[*]12 cucumbers / GCF of 12 = [B]1 cucumber per basket[/B]
[*]24 carrots / GCF of 12 = [B]2 carrots per basket[/B]
[*]36 radishes / GCF of 12 = [B]3 radishes per basket[/B]
[/LIST]
[B][MEDIA=youtube]D1KTOP0h2P4[/MEDIA][/B]

Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What

Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What was the original number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it n.
[LIST]
[*]Start with n
[*]Add 20 to it: n + 20
[*]Double it means we multiply the expression by 2: 2(n + 20)
[*]Get an answer of 53: means an equation, so we set 2(n + 20) equal to 53
[/LIST]
2(n + 20) = 53
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%28n%2B20%29%3D53&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]6.5[/B]

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community col

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community college charges a $35 registration fee plus $375 per course, what is the greatest number of courses for which Angelica can register?
We set up the Tuition function T(c), where c is the number of courses:
T(c) = Cost per course * c + Registration Fee
T(c) = 35c + 375
The problem asks for the number of courses (c) where her tuition [I]cannot exceed[/I] $1000. The phrase [I]cannot exceed[/I] means less than or equal to, or no more than. So we setup the inequality for T(c) <= 1000 below:
35c + 375 <= 1000
To solve this inequality for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=35c%2B375%3C%3D1000&pl=Solve']type it in our search engine and we get[/URL]:
c <= 17.85
Since we cannot have fractional courses, we round down and get:
c[B] <= 17[/B]

Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a t

Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5 Ann paid a total of $49.10.
Set up the cost function C(m) where m is the number of miles:
C(m) = Mileage Rate x m + Tip
2.10m + 5 = 49.10
[URL='https://www.mathcelebrity.com/1unk.php?num=2.10m%2B5%3D49.10&pl=Solve']Type 2.10m + 5 = 49.10 into the search engine[/URL], and we get [B]m = 21[/B].

Anna has 50 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exa

Anna has 50 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exactly four times as many pennies as dimes, how many pennies are in her piggy bank?
Let d be the number of dimes, and p be the number of pennies. We're given:
[LIST=1]
[*]d + p = 50
[*]p = 4d
[/LIST]
Substitute (2) into (1)
d + 4d = 50
[URL='https://www.mathcelebrity.com/1unk.php?num=d%2B4d%3D50&pl=Solve']Type that equation into our search engine[/URL]. We get:
d = 10
Now substitute this into Equation (2):
p = 4(10)
[B]p = 40[/B]

Anna paints a fence in 4 hours wile her brother paints it in 5 hours. If they work together, how lon

Anna paints a fence in 4 hours wile her brother paints it in 5 hours. If they work together, how long will it take them to paint the fence?
Set up unit rates per hour:
[LIST]
[*]Anna paints 1/4 of a fence per hour
[*]Brother paints 1/5 of a fence per hour
[*]Combined, they paint [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Add']1/4 + 1/5[/URL] = 9/20 of a fence per hour
[/LIST]
Setup a proportion of time to hours where h is the number of hours needed to paint the fence
9/20 of a fence the first hour
18/20 of a fence the second hour
2/20 is left. Each 1/20 of the fence takes 60/9 = 6 & 2/3 minutes
6 & 2/3 minutes * 2 = 13 & 1/3 minutes
Final time is:
[B]2 hours and 13 & 1/3 minutes[/B]

Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure

Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure 6 inches wide by 2 feet long, how many boards will she need to complete the job?
Area of platform which is a rectangle:
A = lw
A = 10 * 7
A = 70
Area of boards which are rectangles:
A = lw
A = 2 * 6
A = 12
We divide our platform area by our board area to get the number of boards needed:
Boards needed = Platform Area / Board Area
Boards needed = 70/12
Boards needed = 5.83333
We round up if we want full boards to be [B]6[/B]

Antilog

Calculates the antilog of a number using a base.

April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that

April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that June has. April has two-thirds of the number of sweets that May has. How many sweets does June have?
Let the April sweets be a.
Let the May sweets be m.
Let the June sweets be j.
We're given the following equations:
[LIST=1]
[*]m = 3j/4
[*]a = 2m/3
[*]a + j + m = 90
[/LIST]
Cross multiply #2;
3a = 2m
Dividing each side by 2, we get;
m = 3a/2
Since m = 3j/4 from equation #1, we have:
3j/4 = 3a/2
Cross multiply:
6j = 12a
Divide each side by 12:
a = j/2
So we have:
[LIST=1]
[*]m = 3j/4
[*]a = j/2
[*]a + j + m = 90
[/LIST]
Now substitute equation 1 and 2 into equation 3:
j/2 + j + 3j/4 = 90
Multiply each side by 4 to eliminate fractions:
2j + 4j + 3j = 360
To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%2B4j%2B3j%3D360&pl=Solve']type it in our search engine[/URL] and we get:
j = [B]40[/B]

are all integers whole numbers true or false

are all integers whole numbers true or false
[B]False
[/B]
[LIST]
[*]All whole numbers are integers but not all integers are whole numbers.
[*]Whole numbers are positive integers. Which means negative integers are not whole numbers
[*]-1 for instance is an integer, but not a whole number
[/LIST]

Arnie bought some bagels at 20 cents each. He ate 4, and sold the rest at 30 cents each. His profit

Arnie bought some bagels at 20 cents each. He ate 4, and sold the rest at 30 cents each. His profit was $2.40. How many bagels did he buy?
Let x be the number of bagels Arnie sold. We have the following equation:
0.30(x - 4) - 0.20(4) = 2.40
Distribute and simplify:
0.30x - 1.20 - 0.8 = 2.40
Combine like terms:
0.30x - 2 = 2.40
Add 2 to each side:
0.30x = 4.40
Divide each side by 0.3
[B]x = 14.67 ~ 15[/B]

Aryion has 3 sets of hair ties. Each set contains 2 hair ties. How many hair ties does Aryion have?

Aryion has 3 sets of hair ties. Each set contains 2 hair ties. How many hair ties does Aryion have?
Total hair ties = Sets of hair ties * number of hair ties per set
Total hair ties = 3 * 2
Total hair ties = [B]6[/B]

As a salesperson, you are paid $50 per week plus $2 per sale. This week you want your pay to be at l

As a salesperson, you are paid $50 per week plus $2 per sale. This week you want your pay to be at least $100. What is the minimum number of sales you must make to earn at least $100?
Set up the inequality where s is the amount of sales you make:
50 + 2s >= 100
We use >= because the phrase [I]at least[/I] 100 means 100 or more
Subtract 50 from each side:
2s >= 50
Divide each side by 2
[B]s >= 25[/B]

Ashley deposited $4000 into an account with 2.5% interest, compounded semiannually. Assuming that no

Ashley deposited $4000 into an account with 2.5% interest, compounded semiannually. Assuming that no withdrawals are made, how much will she have in the account after 10 years?
Semiannual means twice a year, so 10 years * 2 times per year = 20 periods. We use this and [URL='https://www.mathcelebrity.com/compoundint.php?bal=4000&nval=20&int=2.50&pl=Semi-Annually']plug the numbers into our compound interest calculator[/URL] to get:
[B]$5,128.15[/B]

Associative Property

Demonstrates the associative property using 3 numbers. Covers the Associative Property of Addition and Associative Property of Multiplication. Also known as the Associative Law of Addition and Associative Law of Multiplication
Numerical Properties

At 1:00 pm you have 24 megabytes of a movie and at 1:15 you have 96 megabytes of a movie. What is th

At 1:00 pm you have 24 megabytes of a movie and at 1:15 you have 96 megabytes of a movie. What is the download rate in megabytes per minute?
First, find the number of minutes:
1:15 - 1:00 = 15 minutes
Next, determine the difference in megabytes
96 - 24 = 72
Finally, determine the download rate:
72 megabytes / 15 minutes = [B]4.8 megabytes per minute[/B]

at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slic

at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slices of pie costs $20.20. what is the cost of one cupcake?
Let the number of cupcakes be c
Let the number of pie slices be p
Total Cost = Unit cost * quantity
So we're given two equations:
[LIST=1]
[*]1c + 2p = 12.40
[*]2c + 3p = 20.20
[/LIST]
We can solve this system of equations any one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]c = 3.2[/B]
[*]p = 4.6
[/LIST]

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 m

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 more child tickets than adult tickets were sold. If a total of $6360 was collected from the total ticket sale that day, how many child tickets were sold?
Let the number of adult tickets be a. Let the number of child tickets be c. We're given two equations:
[LIST=1]
[*]c = a + 30
[*]6a + 4c = 6360
[/LIST]
Substitute equation (1) into equation (2):
6a + 4(a + 30) = 6360
Multiply through to remove parentheses:
6a + 4a + 120 = 6360
T[URL='https://www.mathcelebrity.com/1unk.php?num=6a%2B4a%2B120%3D6360&pl=Solve']ype this equation into our search engine[/URL] to solve for a and we get:
a = 624
Now substitute a = 624 back into equation (1) to solve for c:
c = 124 + 30
c = [B]154[/B]

At a concert there were 25 more women than men. The total number of people at the concert was 139. F

At a concert there were 25 more women than men. The total number of people at the concert was 139. Find the number of women and the number of men at the concert.
Let men be m and women be w. We're given two equations.
[LIST=1]
[*]w = m + 25
[*]m + w = 139
[/LIST]
Substitute equation (1) into equation (2):
m + m + 25 = 139
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%2B25%3D139&pl=Solve']type this equation into our search engine[/URL] and we get:
m = [B]57
[/B]
To find w, we substitute m = 57 into equation (1):
w = 57 + 25
w = [B]82[/B]

At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert

At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert was 360, what was the total number of audience members?
We're looking for total audience members where [I]20% of what equals 360[/I]?
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=360&pct1=20&pcheck=2&pct2=+70&den1=+80&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Type this expression into our search engine[/URL] and we get:
Audience = [B]1,800[/B]

At a football game, a vender sold a combined total of 117 sodas and hot dogs. The number of hot dogs

At a football game, a vender sold a combined total of 117 sodas and hot dogs. The number of hot dogs sold was 59 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
[U]Let h = number of hot dogs and s = number of sodas. Set up our given equations:[/U]
[LIST=1]
[*]h + s = 117
[*]h = s - 59
[/LIST]
[U]Substitute (2) into (1)[/U]
(s - 59) + s = 117
[U]Combine s terms[/U]
2s - 59 = 117
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2s-59%3D117&pl=Solve']equation solver[/URL], we find:[/U]
[B]s = 88
[/B]
[U]Plug s = 88 into (2)[/U]
h = 88 - 59
[B]h = 29[/B]

At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers fo

At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers for $1.35 each. They sold 40 more slices of pizza than hamburgers, and sales totaled $292.5. How many slices of pizza did they sell
Let the number of pizza slices be p and the number of hamburgers be h. We're given two equations:
[LIST=1]
[*]p = h + 40
[*]1.35h + 0.75p = 292.50
[/LIST]
[I]Substitute[/I] equation (1) into equation (2) for p:
1.35h + 0.75(h + 40) = 292.50
1.35h + 0.75h + 30 = 292.50
2.10h + 30 = 292.50
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.10h%2B30%3D292.50&pl=Solve']plug this equation into our search engine[/URL] and we get:
h = 125
The problem asks for number of pizza slices sold (p). So we substitute our value above of h = 125 into equation (1):
p = 125 + 40
p = [B]165[/B]

At a light bulb factory 4 out of every 25 light bulbs are defective. How many light bulbs would you

At a light bulb factory 4 out of every 25 light bulbs are defective. How many light bulbs would you excpect to be defective out of 350 light bulbs
Set up a proportion of light bulbs to defects where d is the number of defects per 350 light bulbs:
4/25 = b/350
[URL='https://www.mathcelebrity.com/prop.php?num1=4&num2=b&den1=25&den2=350&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
b = [B]56[/B]

At a local fitness center, members pay a $10 membership fee and $3 for each aerobics class. Nonme

At a local fitness center, members pay a $10 membership fee and $3 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
Set up the cost functions where x is the number of aerobics classes:
[LIST]
[*]Members: C(x) = 10 + 3x
[*]Non-members: C(x) = 5x
[/LIST]
Set them equal to each other
10 + 3x = 5x
Subtract 3x from both sides:
2x = 10
Divide each side by 2
[B]x = 5 classes[/B]

At a local fitness center, members pay an $8 membership fee and $3 for each aerobics class. Nonmembe

At a local fitness center, members pay an $8 membership fee and $3 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members be equal to nonmembers?
Set up two cost equations C(x):
[LIST=1]
[*]Members: C(x) = 8 + 3x
[*]Nonmembers: C(x) = 5x
[/LIST]
Set the two cost equations equal to each other:
8 + 3x = 5x
Subtract 3x from each side
2x = 8
Divide each side by 2
[B]x = 4[/B]

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2.

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2.
[LIST]
[*]How many men at the party?
[*]How many ladies at the party?
[*]How many kids at the party?
[/LIST]
Our total ratio denominator is 4 + 3 + 2 = 9. To find the number of each type of person, we take their ratio divided by their ratio numerator times 72 people at the party
[U]Calculate ratios:[/U]
[LIST]
[*]Men: [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F9&frac2=72&pl=Multiply']4/9 * 72[/URL] = [B]32[/B]
[*]Ladies: [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F9&frac2=72&pl=Multiply']3/9 * 72[/URL] = [B]24[/B]
[*]Kids: [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F9&frac2=72&pl=Multiply']2/9 * 72[/URL] = [B]16[/B]
[/LIST]
[U]Check our work:[/U]
Men + Ladies + Kids = 32 + 24 + 16
Men + Ladies + Kids = 72 <-- This checks out!

At a recent motorcycle rally, the number of men exceeded the number of women by 247. If x represents

At a recent motorcycle rally, the number of men exceeded the number of women by 247. If x represents the number of women, write an expression for the number of men.
[B]m = x + 247[/B]

At Costco, a case of 12 boxes of macaroni and cheese costs $18.00. How much is each box of macaroni

At Costco, a case of 12 boxes of macaroni and cheese costs $18.00. How much is each box of macaroni and cheese worth?
Cost per box = Total price / number of boxes
Cost per box = $18/12
Cost per box = [B]$1.50[/B]

At Sams Club, 32 cans of Coke cost a total of $8.96. What is the cost per can?

At Sams Club, 32 cans of Coke cost a total of $8.96. What is the cost per can?
Unit Cost is Total Cost / Number of Units
Unit Cost = $8.96/32
Unit Cost = [B]$0.28[/B]

At the beginning of Jack's diet, he was 257 pounds. If he lost 3 pounds per week, find his weight af

At the beginning of Jack's diet, he was 257 pounds. If he lost 3 pounds per week, find his weight after 12 weeks.
A loss of weight means we subtract from Jack's current weight.
New Weight = Current Weight - Weight Loss per week * number of weeks
New Weight =257 - 3*12
New Weight =257 - 36
New Weight =[B] 221[/B]

At the end of the 2021 NBA season, the NY Knicks had 10 more wins than losses. This NBA season the N

At the end of the 2021 NBA season, the NY Knicks had 10 more wins than losses. This NBA season the NY Knicks played a total of 72 times. Find a solution to this problem and explain.
Let w be the number of wins
Let l be the number of losses
We're given two equations:
[LIST=1]
[*]w = l + 10
[*]l + w = 72
[/LIST]
To solve this system of equations, substitute equation (1) into equation (2) for w:
l + l + 10 = 72
To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l%2Bl%2B10%3D72&pl=Solve']type it in our math engine[/URL] and we get:
l = [B]31
[/B]
To solve for w, we substitute l = 31 into equation (1):
w = 31 + 10
w = [B]41[/B]

At the movie theater, Celeste bought 2 large drinks and 2 large popcorns for $8.50. She paid with a

At the movie theater, Celeste bought 2 large drinks and 2 large popcorns for $8.50. She paid with a twenty-dollar bill. What is the fewest number of bills and coins that she could have received as change?r of bills and coins that she could have received as change?
Calculate change:
Change = Amount Paid - Bill
Change = $20.00 - $8.50
Change = $11.50
Largest bill we can start with is a 10 dollar bill:
$11.50 - 10 = $1.50
Next largest bill is a $1 bill
$1.50 - $1 = 0.50
Now we're down to coins. Largest coin(s) we can use are quarters (assuming no half-dollars)
2 quarters equals 0.50
0.50 - 0.50 = 0
[U]Therefore, our answer is:[/U]
[B]Ten dollar Bill, 1 dollar bill, and 2 quarters[/B]

Austin has 15 CDs, which is 3 less than his sister has. How many CDs does his sister have?

Austin has 15 CDs, which is 3 less than his sister has. How many CDs does his sister have?
Let s be the number of CD's his sister has and a be the number Austin has
[LIST=1]
[*]a = 15
[*]a = s - 3
[/LIST]
Substitute (1) into (2)
15 = s - 3
Add 3 to each side
[B]s = 18[/B]

Austin needs $240 to buy a new bike if he can save $16 per week and how many weeks can you purchase

Austin needs $240 to buy a new bike if he can save $16 per week and how many weeks can you purchase the bike?
Set up the equation, where w equals the number of weeks needed. We have:
16w = 240
[URL='https://www.mathcelebrity.com/1unk.php?num=16w%3D240&pl=Solve']Typing this into our search engine[/URL], we get [B]w = 15[/B].

Automorphic Number

This calculator determines the nth automorphic number

b more points than 75

b more points than 75
Let b be the number of points
b + 75

Babylonian Method

Determines the square root of a number using the Babylonian Method.

Bacteria in a petra dish doubles every hour. If there were 34 bacteria when the experiment began, wr

Bacteria in a petra dish doubles every hour. If there were 34 bacteria when the experiment began, write an equation to model this.
Let h be the number of hours since the experiment began. Our equation is:
[B]B(h) = 34(2^h)[/B]

Balancing Equations

Given 4 numbers, this will use the four operations: addition, subtraction, multiplication, or division to balance the equations if possible.

Balls numbered 1 to 10 are placed in a bag. Two of the balls are drawn out at random. Find the proba

Balls numbered 1 to 10 are placed in a bag. Two of the balls are drawn out at random. Find the probability that the numbers on the balls are consecutive.
Build our sample set:
[LIST]
[*](1, 2)
[*](2, 3)
[*](3, 4)
[*](4, 5)
[*](5, 6)
[*](6, 7)
[*](7, 8)
[*](8, 9)
[*](9, 10)
[/LIST]
Each of these 9 possibilities has a probability of:
1/10 * 1/9
This is because we draw without replacement. To start, the bag has 10 balls. On the second draw, it only has 9. We multiply each event because each draw is independent.
We have 9 possibilities, so we have:
9 * 1/10 * 1/9
Cancelling, the 9's, we have [B]1/10[/B]

Barbara bought a piece of rope that was 7 1/3 meters long. She cut the rope into 3 equal pieces. How

Barbara bought a piece of rope that was 7 1/3 meters long. She cut the rope into 3 equal pieces. How long is each piece of rope?
Using our mixed number converter, we see that:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=7%261%2F3&frac2=3%2F8&pl=Simplify']7&1/3[/URL] = 22/3
Split into [URL='https://www.mathcelebrity.com/fraction.php?frac1=22%2F9&frac2=3&pl=Simplify']3 equal pieces[/URL], we have:
22/3 / 3 = 22/9 or 2&4/9

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants co

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants cost $4 each. If she plans to spend at least $20 and purchase less than 15 plants in total, create a system of equations or inequalities that model the situation. Define the variables you use.
[U]Define variables[/U]
[LIST]
[*]Let c be the number of corn plants
[*]Let p be the number of potato plants
[/LIST]
Since cost = price * quantity, we're given two inequalities:
[LIST=1]
[*][B]3p + 4c >= 20 (the phrase [I]at least[/I] means greater than or equal to)[/B]
[*][B]c + p < 15[/B]
[/LIST]

Barney has $450 and spends $3 each week. Betty has $120 and saves $8 each week. How many weeks will

Barney has $450 and spends $3 each week. Betty has $120 and saves $8 each week. How many weeks will it take for them to have the same amount of money?
Let w be the number of weeks that go by for saving/spending.
Set up Barney's balance equation, B(w). Spending means we [U]subtract[/U]
B(w) = Initial Amount - spend per week * w weeks
B(w) = 450 - 3w
Set up Betty's balance equation, B(w). Saving means we [U]add[/U]
B(w) = Initial Amount + savings per week * w weeks
B(w) = 120 + 8w
The same amount of money means both of their balance equations B(w) are equal. So we set Barney's balance equal to Betty's balance and solve for w:
450 - 3w = 120 + 8w
Add 3w to each side to isolate w:
450 - 3w + 3w = 120 + 8w + 3w
Cancelling the 3w on the left side, we get:
450 = 120 + 11w
Rewrite to have constant on the right side:
11w + 120 = 450
Subtract 120 from each side:
11w + 120 - 120 = 450 - 120
Cancelling the 120's on the left side, we get:
11w = 330
To solve for w, we divide each side by 11
11w/11 = 330/11
Cancelling the 11's on the left side, we get:
w = [B]30
[MEDIA=youtube]ifG_q-utgJI[/MEDIA][/B]

Base Conversion Operations

This calculator allows you to add, subtract, multiply, and divide two numbers with different bases.

Basic Math Operations

Given 2 numbers, this performs the following arithmetic operations:

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

Basic Statistics

Given a number set, and an optional probability set, this calculates the following statistical items:

Expected Value

Mean = μ

Variance = σ^{2}

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Expected Value

Mean = μ

Variance = σ

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign

Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign, then divided by 3. What was the original equation
[LIST=1]
[*]If we added 7 to both sides, that means we had a minus 7 (-7) to start with as a constant. Since subtraction undoes addition.
[*]If we divided by 3, this means we multiplied x by 3 to begin with. Since division undoes multiplication
[/LIST]
So we have the start equation:
3x - 7
If the answer was x = -4, then we plug this in to get our number on the right side of the equation:
3(-4) - 7
-12 - 7
-19
This means our original equation was:
[B]3x - 7 = -19[/B]
And if we want to solve this to prove our answer, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D-19&pl=Solve']type the equation into our search engine [/URL]and we get:
x = -4

Before Barry Bonds, Mark McGwire, and Sammy Sosa, Roger Maris held the record for the most home runs

Before Barry Bonds, Mark McGwire, and Sammy Sosa, Roger Maris held the record for the most home runs in one season. Just behind Maris was Babe Ruth. The numbers of home runs hit by these two athletes in their record-breaking seasons form consecutive integers. Combined, the two athletes hit 121 home runs. Determine the number of home runs hit by Maris and Ruth in their record-breaking seasons.
We want [URL='https://www.mathcelebrity.com/consecintwp.php?num=121&pl=Sum']the sum of 2 consecutive integers equals 121[/URL].
[B]We get Maris at 61 and Ruth at 60[/B]

Belen can make 15 necklaces in 3 1/2 hours. How many can she make in one hour?

Belen can make 15 necklaces in 3 1/2 hours. How many can she make in one hour?
We set up a proportion of necklaces to time, where n is the number of necklaces Belen can make in 1 hour:
3 & 1/2 = 3.5, so we have:
15/3.5 = n/1
[SIZE=3][FONT=Helvetica][COLOR=rgb(34, 34, 34)]
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=n&den1=3.5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine and we ge[/URL]t:
n = [B]4.29 hours[/B][/COLOR][/FONT][/SIZE]

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each p

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each pencil
The cost per pencil is:
1560/30 = 52
Build revenue function:
Revenue = Number of Pencils * Sales Price (s)
Revenue = 30s
The profit equation is:
Profit = Revenue - Cost
Given profit is 180 and cost is 1560, we have:
30s - 1560 = 180
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=30s-1560%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
s = 58
This is sales for total profit. The question asks profit per pencil.
Profit per pencil = Revenue per pencil - Cost per pencil
Profit per pencil = 58 - 52
Profit per pencil = [B]6[/B]

Ben can write 153 letters in 3 minutes. At this rate, how many letters can he write in 10 minutes?

Ben can write 153 letters in 3 minutes. At this rate, how many letters can he write in 10 minutes?
We set up a proportion of letters to minutes where the number of letters in 10 minutes is l:
153/3 = l/10
We [URL='https://www.mathcelebrity.com/prop.php?num1=153&num2=l&den1=3&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into a search engine[/URL] and we get:
l =[B] 510[/B]

Ben has $4.50 in quarters(Q) and dimes(D). a)Write an equation expressing the total amount of money

Ben has $4.50 in quarters(Q) and dimes(D). a)Write an equation expressing the total amount of money in terms of the number of quarters and dimes. b)Rearrange the equation to isolate for the number of dimes (D)
a) The equation is:
[B]0.1d + 0.25q = 4.5[/B]
b) Isolate the equation for d. We subtract 0.25q from each side of the equation:
0.1d + 0.25q - 0.25q = 4.5 - 0.25q
Cancel the 0.25q on the left side, and we get:
0.1d = 4.5 - 0.25q
Divide each side of the equation by 0.1 to isolate d:
0.1d/0.1 = (4.5 - 0.25q)/0.1
d = [B]45 - 2.5q[/B]

Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of

Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 47 cards left. How many cards did Benny start with?
Let b be the number of baseball trading cards Benny started with. We have the following events:
[LIST=1]
[*]Benny buys 8 new cards, so we add 8 to get b + 8
[*]The dog ate half of his cards the next day, so Benny has (b + 8)/2
[*]We're told he has 47 cards left, so we set (b + 8)/2 equal to 47
[/LIST]
(b + 8)/2 = 47
[B][U]Cross multiply:[/U][/B]
b + 8 = 47 * 2
b + 8 = 94
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B8%3D94&pl=Solve']Type this equation into the search engine[/URL], we get [B]b = 86[/B].

Bernoulli Trials

Given a success probability p and a number of trials (n), this will simulate Bernoulli Trials and offer analysis using the Bernoulli Distribution. Also calculates the skewness, kurtosis, and entropy

Beverly has $50 to spend at an amusement park. She plans to spend $10 for food, and $15 for admissio

Beverly has $50 to spend at an amusement park. She plans to spend $10 for food, and $15 for admission to the park. Each ride costs $1.50 to ride. Write an inequality to represent the possible number of rides she can ride?
First, we subtract the food and admission cost from Beverly's starting balance of $50:
Cost available for rides = Starting Balance - Food - Admission
Cost available for rides = 50 - 10 - 15
Cost available for rides = 25
Now we set up an inequality for the number of rides (r) that Beverly can ride with the remaining balance:
1.50r <= 25
To solve for r, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.50r%3C%3D25&pl=Show+Interval+Notation']type this inequality into our search engine[/URL] and we get:
[B]r <=[/B] [B]16.67[/B]

Big John weighs 300 pounds and is going on a diet where he'll lose 3 pounds per week. Write an equat

Big John weighs 300 pounds and is going on a diet where he'll lose 3 pounds per week. Write an equation in slope-intercept form to represent this situation.
[LIST]
[*]The slope intercept form is y = mx + b
[*]y is John's weight
[*]x is the number of weeks
[*]A 3 pound per week weight loss means -3 as the coefficient m
[*]b = 300, John's starting weight
[/LIST]
[B]y = -3x + 300[/B]

Bike rental shop A charges $20 per kilometre travelled with no additional fee. Bike rental shop B ch

Bike rental shop A charges $20 per kilometre travelled with no additional fee. Bike rental shop B charges only $8 per kilometre travelled, but has a starting charge of $35. If Bob plans to travel 7km by bike, which rental shop should he choose for a better price
[U]Shop A Cost function C(k) where k is the number of kilometers used[/U]
C(k) = Cost per kilometer * k + Starting Charge
C(k) = 20k
With k = 7, we have:
C(7) = 20 * 7
C(7) = 140
[U]Shop B Cost function C(k) where k is the number of kilometers used[/U]
C(k) = Cost per kilometer * k + Starting Charge
C(k) = 8k + 35
With k = 7, we have:
C(7) = 8 * 7 + 35
C(7) = 56 + 35
C(7) = 91
Bog should choose [B]Shop B[/B] since they have the better price for 7km

Bills car rental charges a base fee of 50$ and then $0.20 per mile

Bills car rental charges a base fee of 50$ and then $0.20 per mile.
Set up the cost function C(m) where m is the number of miles driven:
[B]C(m) = 50 + 0.20m[/B]

Binomial Distribution

Calculates the probability of 3 separate events that follow a binomial distribution. It calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness and kurtosis.

Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor

Calculates moment number t using the moment generating function

Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor

Calculates moment number t using the moment generating function

Bit Shifting

Performs a bit shift left or a bit shift right on a decimal or binary number

Bitwise Operations

Performs bitwise operations between two decimal or binary numbers:

* Bitwise OR

* Bitwise AND

* Bitwise XOR

Also performs Bitwise NOT on 1 number

* Bitwise OR

* Bitwise AND

* Bitwise XOR

Also performs Bitwise NOT on 1 number

Blackjack Card Counting

This calculator allows you to enter a number of players with one deck of cards by simulating an opening blackjack deal using card counting methods.

Blake and Tatsu are each assigned a paper for a class they share. Blake decides to write 4 pages at

Blake and Tatsu are each assigned a paper for a class they share. Blake decides to write 4 pages at a time while Tatsu decides to write 7 pages at a time. If they end up writing the same number of pages, what is the smallest number of pages that the papers could have had?
We want the least common multiple of 4 and 7, written as LCM(4, 7). Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=7&num3=&pl=LCM']LCM Calculator[/URL], we get:
LCM(4, 7) = [B]28 pages[/B]

Blake writes 4 pages per hour. How many hours will Blake have to spend writing this week in order to

Blake writes 4 pages per hour. How many hours will Blake have to spend writing this week in order to have written a total of 16 pages?
[U]Let x = the number of hours Blake needs to write[/U]
4 pages per hour * x hours = 16
[U]Divide each side by 4[/U]
[B]x = 4 hours[/B]

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 fe

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 feet. Use the perimeter formula to find the width of the rectangular yard in inches: P = 2L + 2W.
Plugging our numbers in for P = 22 and L = 5, we get:
22 = 2(5) + 2W
22 = 10 + 2w
Rewritten, we have:
10 + 2w = 22
[URL='https://www.mathcelebrity.com/1unk.php?num=10%2B2w%3D22&pl=Solve']Plug this equation into the search engine[/URL], we get:
[B]w = 6[/B]

Bob finished reading his book in x days. Each day, he read 4 pages. His book has 28 pages

Bob finished reading his book in x days. Each day, he read 4 pages. His book has 28 pages
Our equation for this is found by multiplying pages per day times number of days;
4x = 28
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3D28&pl=Solve']we type the equation into our search engine[/URL] and we get:
x = [B]7[/B]

Bob has a bookcase with 4 shelves. There are k books on each shelf. Using k, write an expression for

Bob has a bookcase with 4 shelves. There are k books on each shelf. Using k, write an expression for the total number of books.
Total Books = Bookcases * shelves per bookcase * books per shelf
Total Books = 1 * 4 * k
Total Books = [B]4k[/B]

Bob has half as many quarters as dimes. He has $3.60. How many of each coin does he have?

Bob has half as many quarters as dimes. He has $3.60. How many of each coin does he have?
Let q be the number of quarters. Let d be the number of dimes. We're given:
[LIST=1]
[*]q = 0.5d
[*]0.25q + 0.10d = 3.60
[/LIST]
Substitute (1) into (2):
0.25(0.5d) + 0.10d = 3.60
0.125d + 0.1d = 3.6
Combine like terms:
0.225d = 3.6
[URL='https://www.mathcelebrity.com/1unk.php?num=0.225d%3D3.6&pl=Solve']Typing this equation into our search engine[/URL], we're given:
[B]d = 16[/B]
Substitute d = 16 into Equation (1):
q = 0.5(16)
[B]q = 8[/B]

Braille Translator

Given a phrase with letters, numbers, and most punctuation symbols, the calculator will perform the following duties:

1) Translate that phrase to Braille

2) Calculate the number of dots in the message

3) Calculate the number of empty spaces in the message

1) Translate that phrase to Braille

2) Calculate the number of dots in the message

3) Calculate the number of empty spaces in the message

Bridget can grow 6 flowers with every seed packet. With 4 seed packets, how many total flowers can B

Bridget can grow 6 flowers with every seed packet. With 4 seed packets, how many total flowers can Bridget have in her garden?
Set up a proportion of flowers to seed packets where f is the number of flowers for 4 seed packets. We have:
6/1 = f/4
Cross multiply:
f(1) = 24
f = 24

Brighthouse charges $120 a month for their basic plan, plus $2.99 for each on demand movie you buy.

Brighthouse charges $120 a month for their basic plan, plus $2.99 for each on demand movie you buy. Write and solve and inequality to find how many on demand movies could you buy if you want your bill to be less than $150 for the month.
Let x equal to the number room movie rentals per month. Our inequality is:
120 + 2.99x < 150
To solve for the number of movies, Add 120 to each side
2.99x < 30
Divide each side by 2.99
x < 10.03, which means 10 since you cannot buy a fraction of a movie

can you continue this pattern 1,5,13,29

can you continue this pattern 1,5,13,29
Looking at the numbers, we see a pattern of the next number as the prior number * 2 and then add 3
With each term as t(n), we find t(n + 1) as:
t(n + 1) = [B]2*t(n) + 3[/B]
t(2) = 2(1) + 3 = 2 + 3 = 5
t(3) = 2(5) + 3 = 10 + 3 = 13
t(4) = 2(13) + 3 = 26 + 3 = 29
t(5) = 2(29) + 3 = 58 + 3 = [B]61[/B]

Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly hav

Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly have in her backyard? Solve using unit rates.
Set up a proportion of plants per seed packets where p is the number of plants per 37 seed packets.
50/25 = p/37
Copying and pasting this problem [URL='http://www.mathcelebrity.com/prop.php?num1=50&num2=p&den1=25&den2=37&propsign=%3D&pl=Calculate+missing+proportion+value']into our search engine[/URL], we get [B]p = 74[/B].

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Let m be the number of months. We have the pages written function P(m) as:
P(m) = 12m + 35
The problem asks for P(5):
P(5) = 12(5) + 35
P(5) = 60 + 35
P(5) = [B]95[/B]

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month unti

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Set up the equation where m is the number of months:
pages per month * m + pages written already
12m + 35
The problems asks for m = 5:
12(5) + 35
60 + 35
[B]95 pages[/B]

Carmen is serving her child french fries and chicken wings for lunch today. Let f be the number of f

Carmen is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Carmen wants the total calorie count from the french fries and chicken wings to be less than 500 calories. Using the values and variables given, write an inequality describing this.
We have:
25f + 100c < 50
Note: We use < and not <= because it states less than in the problem.

Cars and trucks are the most popular vehicles. last year, the number of cars sold was 39,000 more th

Cars and trucks are the most popular vehicles. last year, the number of cars sold was 39,000 more than 3 times the number of trucks sold. There were 216,000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year.
Let c be the number of cars.
Let t be the number of trucks.
We're given two equations:
[LIST=1]
[*]c = 3t + 39000
[*]c + t = 216000
[/LIST]
Substitute equation (1) into equation (2) for c:
3t + 39000 + t = 216000
To solve this equation for t, [URL='https://www.mathcelebrity.com/1unk.php?num=3t%2B39000%2Bt%3D216000&pl=Solve']we type it in our math engine [/URL]and we get:
t = [B]44,250[/B]

Casey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double her

Casey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double her daughter's age
Declare variables for each age:
[LIST]
[*]Let Casey's age be c
[*]Let her daughter's age be d
[*]Let n be the number of years from now where Casey will be double her daughter's age
[/LIST]
We're told that:
26 + n = 2(4 + n)
26 + n = 8 + 2n
Solve for [I]n[/I] in the equation 26 + n = 8 + 2n
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables n and 2n. To do that, we subtract 2n from both sides
n + 26 - 2n = 2n + 8 - 2n
[SIZE=5][B]Step 2: Cancel 2n on the right side:[/B][/SIZE]
-n + 26 = 8
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 26 and 8. To do that, we subtract 26 from both sides
-n + 26 - 26 = 8 - 26
[SIZE=5][B]Step 4: Cancel 26 on the left side:[/B][/SIZE]
-n = -18
[SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE]
-1n/-1 = -18/-1
n = [B]18[/B]
Check our work for n = 18:
26 + 18 ? 8 + 2(18)
44 ? 8 + 36
44 = 44

Cassidy is renting a bicycle on the boardwalk. The rental costs a flat fee of $10 plus an additional

Cassidy is renting a bicycle on the boardwalk. The rental costs a flat fee of $10 plus an additional $7 per hour. Cassidy paid $45 to rent a bicycle.
We set up the cost equation C(h) where h is the number of hours of rental:
C(h) = hourly rental rate * h + Flat Fee
C(h) = 7h + 10
We're told that Cassidy paid 45 to rent a bicycle, so we set C(h) = 45
7h + 10 = 45
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=7h%2B10%3D45&pl=Solve']type this equation into our math engine[/URL] and we get:
h = [B]5[/B]

Cathy wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another

Cathy wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another gym has no joining fee and costs $60 per month. a. In how many months will both gym memberships cost the same? What will that cost be?
Set up cost equations where m is the number of months enrolled:
[LIST=1]
[*]C(m) = 35m + 150
[*]C(m) = 60m
[/LIST]
Set them equal to each other:
35m + 150 = 60m
[URL='http://www.mathcelebrity.com/1unk.php?num=35m%2B150%3D60m&pl=Solve']Pasting the equation above into our search engine[/URL], we get [B]m = 6[/B].

Ceiling

Calculates the ceiling of a number

Chang is serving his child french fries and chicken wings for lunch today. Let f be the number of f

Chang is serving his child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Chang wants the total calorie count from the french fries and chicken wings to be less than 600 calories. Using the values and variables given, write an inequality describing this.
We have [B]25f + 100c < 600[/B] as our inequality.

Change Base 10 number of 25 into base 2

Change Base 10 number of 25 into base 2
Using our [URL='https://www.mathcelebrity.com/binary.php?num=25&check1=7&bchoice=2&pl=Convert']base change calculator[/URL], we get:
25 = [B]11001[/B] (in base 2)

Change the base 10 number 100 into base 5

Change the base 10 number 100 into base 5
Using our [URL='https://www.mathcelebrity.com/binary.php?num=100&check1=7&bchoice=5&pl=Convert']base change calculator[/URL], we get:
100 = [B]400 (Base 5)[/B]

Change the base 2 number 1000 into base 10

Change the base 2 number 1000 into base 10
1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 0 * 2^0
8 + 0 + 0 + 0 = [B]8[/B]

Charlene wants to invest $10,000 long enough for it to grow to at least $20000. The compound interes

Charlene wants to invest $10,000 long enough for it to grow to at least $20,000. The compound interest rate is 6% p.a. How many whole number of years does she need to invest the money for so that it grows to her $20,000 target?
We want 10,000(1.06)^n = 20,000.
But what the problem asks for is how long it will take money to double. We can use a shortcut called the Rule of 72. [URL='https://www.mathcelebrity.com/rule72.php?num=6&pl=Calculate']Using the Rule of 72 at 6%[/URL], we get [B]12 years[/B].

Charlie buys a 40 pound bag of cat food. His cat eats a 1/2 pound of food per day.

Charlie buys a 40 pound bag of cat food. His cat eats a 1/2 pound of food per day.
Set up an equation:
1/2x = 40 where x is the number of days
Multiply through by 2
[B]x = 80[/B]

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the t

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the tank has at least 58 liters. What are the possible numbers of minutes Charmaine could add water?
This is an algebraic inequality. The phrase [I]at least[/I] means greater than or equal to. So we have:
6m + 16 >= 58 <-- This is our algebraic expression/inequality.
To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=6m%2B16%3E%3D58&pl=Solve']we type this into our search engine [/URL]and we get:
[B]m >= 7[/B]

Charrie found a piece of 8 meters rope. She cuts it into equal length. She made three cuts. How long

Charrie found a piece of 8 meters rope. She cuts it into equal length. She made three cuts. How long is each piece of the rope?
Equal length means we divide the length of the rope by the number of equal cuts
[B]8/3 or 2 & 2/3 meters[/B]

Chicken is on sale for $3.90 per pound. If Ms.Gelllar buys 2.25 pounds of chicken, how much will she

Chicken is on sale for $3.90 per pound. If Ms.Gelllar buys 2.25 pounds of chicken, how much will she spend? round to the nearest penny and show your work
Total spend = Cost per pound * Number of pounds
Total spend = $3.90 * 2.25 pounds
Total spend = [B]$8.78[/B] (rounded to 2 digits)

Chuck-a-luck is an old game, played mostly in carnivals and county fairs. To play chuck-a-luck you p

Chuck-a-luck is an old game, played mostly in carnivals and county fairs. To play chuck-a-luck you place a bet, say $1, on one of the numbers 1 through 6. Say that you bet on the number 4. You then roll three dice (presumably honest). If you roll three 4’s, you win $3.00; If you roll just two 4’s, you win $2; if you roll just one 4, you win $1 (and, in all of these cases you get your original $1 back). If you roll no 4’s, you lose your $1. Compute the expected payoff for chuck-a-luck.
Expected payoff for each event = Event Probability * Event Payoff
Expected payoff for 3 matches:
3(1/6 * 1/6 * 1/6) = 3/216 = 1/72
Expected payoff for 2 matches:
2(1/6 * 1/6 * 5/6) = 10/216 = 5/108
Expected payoff for 1 match:
1(1/6 * 5/6 * 5/6) = 25/216
Expected payoff for 0 matches:
-1(5/6 * 5/6 * 5/6) = 125/216
Add all these up:
(3 + 10 + 25 - 125)/216
-87/216 ~ [B]-0.40[/B]

Circular Permutation

Calculates the following:

Number of ways to arrange n distinct items arranged on a circle

Number of ways to arrange n distinct items arranged on a circle

Claire bought 180 candies and 140 pens for goody bags for her birthday. What is the largest number o

Claire bought 180 candies and 140 pens for goody bags for her birthday. What is the largest number of goody bags that Claire can make so that each goody bag has the same number of candies and the same number of pens? (All candies and pens should be used.)
We want the greatest common factor of 180 and 140. When we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=140&num2=180&num3=&pl=GCF+and+LCM']run GCF(180,140) in our calculator[/URL], we get 20.
We divide our total candies and total pens by our GCF. So each bag has the following:
Candies: 180/20 = [B]9 candies[/B]
Pens: 140/20 = [B]7 pens[/B]

Claire makes bracelets using blue and red beads.Each bracelet has 20 red beads and 5 blue beads.Writ

Claire makes bracelets using blue and red beads.Each bracelet has 20 red beads and 5 blue beads.Write an ordered pair to represent the number of red beads and blue beads Claire will use to make 8 bracelets.
8 bracelets gives you 8 x 20 = 160 red beads and 8 * 5 = 40 blue beads.
The ordered pair is[B] (160, 40)[/B]

Clara can bake 17 cookies with each scoop of flour. With two scoops of flour, how many cookies can C

Clara can bake 17 cookies with each scoop of flour. With two scoops of flour, how many cookies can Clara bake?
Set up a proportion where x is the number of cookies per 2 scoops of flour
17 cookies/1 scoop = x cookies/2 scoops
[URL='http://www.mathcelebrity.com/prop.php?num1=17&num2=x&den1=1&den2=2&propsign=%3D&pl=Calculate+missing+proportion+value']Running this in the search engine, we get[/URL]:
[B]x = 34 cookies[/B]

Clark wants to give some baseball cards to his friends. If he gives 6 cards to each of his friends,

Clark wants to give some baseball cards to his friends. If he gives 6 cards to each of his friends, he will have 5 cards left. If he gives 8 cards to each of his friends, he will need 7 more cards. How many friends is the giving the cards to?
Let the number of friends Clark gives his cards to be f. Let the total amount of cards he gives out be n. We're given 2 equations:
[LIST=1]
[*]6f + 5 = n
[*]8f - 7 = n
[/LIST]
Since both equations equal n, we set these equations equal to each other
6f + 5 = 8f - 7
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=6f%2B5%3D8f-7&pl=Solve']type this equation into our search engine[/URL] and we get:
f = [B]6
[/B]
To check our work, we plug in f = 6 into each equation:
[LIST=1]
[*]6(6) + 5 = 36 + 5 = 41
[*]8(6) - 7 = 48 - 7 = 41
[/LIST]
So this checks out. Clark has 41 total cards which he gives to 6 friends.

Coach vega orders 30 bats for the team. He orders 7 oak, 7 maple, 12 ash bats, and and some bamboo b

Coach vega orders 30 bats for the team. He orders 7 oak, 7 maple, 12 ash bats, and and some bamboo bats. Find b, the number of bamboo bats.
30 bats - 7 maple - 7 oak - 12 ash
30 - 26 = [B]4 bamboo bats[/B]

Colin was thinking of a number. Colin divides by 8, then adds 1 to get an answer of 2. What was the

Colin was thinking of a number. Colin divides by 8, then adds 1 to get an answer of 2. What was the original number?
Let the number be n.
Divide by 8:
n/8
Then add 1:
n/8 + 1
The phrase [I]get an answer[/I] of means an equation, so we set n/8 + 1 equal to 2:
n/8 + 1 = 2
To solve for n, we subtract 1 from each side to isolate the n term:
n/8 + 1 - 1 = 2 - 1
Cancel the 1's on the left side, we get:
n/8 = 1
Cross multiply:
n = 8*1
n = [B]8[/B]

Collatz Conjecture

Takes any natural number using the Collatz Conjecture and reduces it down to 1.

Commutative Property

Demonstrates the commutative property of addition and the commutative property of multiplication using 3 numbers.
Numerical Properties

Company a charges $25 plus $0.10 a mile. Company b charges $20 plus $0.15 per mile. How far would yo

Company a charges $25 plus $0.10 a mile. Company b charges $20 plus $0.15 per mile. How far would you need to travel to get each charge to be the same?
Let x be the number of miles traveled
Company A charge: C = 25 + 0.10x
Company B charge: C = 20 + 0.15x
Set up an equation find out when the charges are the same.
25 + 0.10x = 20 + 0.15x
Combine terms and simplify
0.05x = 5
Divide each side of the equation by 0.05 to isolate x
x = [B]100[/B]

Company A rents copy machines for $300 a month plus $0.05 per copy. Company B charges $600 plus $0.0

Company A rents copy machines for $300 a month plus $0.05 per copy. Company B charges $600 plus $0.01 per copy. For which number of copies do the two companies charge the same amount?
With c as the number of copies, we have:
Company A Cost = 300 + 0.05c
Company B Cost = 600 + 0.01c
Set them equal to each other
300 + 0.05c = 600 + 0.01c
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=300%2B0.05c%3D600%2B0.01c&pl=Solve']equation solver[/URL] to get:
[B]c = 7,500[/B]

Comparison of Numbers

Compares two numbers and checks to see if they are equal to one another, if the first number is greater than the second number, or the first number is less than the second number. Minimum and maximum.

Complex Number Operations

Given two numbers in complex number notation, this calculator:

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

Composite Number

This calculator determines the nth composite number. Helps you generate composite numbers.

Compound Interest and Annuity Table

Given an interest rate (i), number of periods to display (n), and number of digits to round (r), this calculator produces a compound interest table. It shows the values for the following 4 compound interest annuity functions from time 1 to (n) rounded to (r) digits:

v^{n}

d

(1 + i)^{n}

a_{n|}

s_{n|}

ä_{n|i}

s_{n|i}

Force of Interest δ^{n}

v

d

(1 + i)

a

s

ä

s

Force of Interest δ

Compute a 75% Chebyshev interval around the mean for x values and also for y values.

Compute a 75% Chebyshev interval around the mean for [I]x[/I] values and also for [I]y[/I] values.
[B][U]Grid E: [I]x[/I] variable[/U][/B]
11.92 34.86 26.72 24.50 38.93 8.59 29.31
23.39 24.13 30.05 21.54 35.97 7.48 35.97
[B][U]Grid H: [I]y[/I] variable[/U][/B]
27.86 13.29 33.03 44.31 16.58 42.43
39.61 25.51 39.14 16.58 47.13 14.70 57.47 34.44
According to Chebyshev's Theorem,
[1 - (1/k^2)] proportion of values will fall between Mean +/- (k*SD)
k in this case equal to z
z = (X-Mean)/SD
X = Mean + (z*SD)
1 - 1/k^2 = 0.75
- 1/k^2 = 0.75 - 1= - 0.25
1/k^2 = 0.25
k^2 = 1/0.25
k^2 = 4
k = 2
Therefore, z = k = 2
First, [URL='http://www.mathcelebrity.com/statbasic.php?num1=11.92%2C34.86%2C26.72%2C24.50%2C38.93%2C8.59%2C29.31%2C23.39%2C24.13%2C30.05%2C21.54%2C35.97%2C7.48%2C35.97&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']determine the mean and standard deviation of x[/URL]
Mean(x) = 25.24
SD(x) = 9.7873
Required Interval for x is:
Mean - (z * SD) < X < Mean + (z * SD)
25.24 - (2 * 9.7873) < X < 25.24 - (2 * 9.7873)
25.24 - 19.5746 < X < 25.24 + 19.5746
5.6654 < X < 44.8146
Next, [URL='http://www.mathcelebrity.com/statbasic.php?num1=27.86%2C13.29%2C33.03%2C44.31%2C16.58%2C42.43%2C39.61%2C25.51%2C39.14%2C16.58%2C47.13%2C14.70%2C57.47%2C34.44&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']determine the mean and standard deviation of y[/URL]
Mean(y) = 32.29
SD(y) = 9.7873
Required Interval for y is:
Mean - (z * SD) < Y < Mean + (z * SD)
32.29 - (2 * 13.1932) < Y < 32.29 - (2 * 13.1932)
32.29 - 26.3864 < Y < 32.29 + 26.3864
5.9036 < X < 58.6764

Concert tickets cost $14.95 each. Which expression represents the total cost of 25 tickets?

Concert tickets cost $14.95 each. Which expression represents the total cost of 25 tickets?
Calculate Total Cost:
Total Cost = Cost Per Ticket * Number of Tickets
Total Cost = $14.95 * 25
Total Cost = [B]$373.75[/B]

Congratulations!! You are hired at Roof and Vinyl Housing Systems. Your starting salary is $45,600 f

Congratulations!! You are hired at Roof and Vinyl Housing Systems. Your starting salary is $45,600 for the year. Each year you stay employed with them your salary will increase by 3.5%. Determine what your salary would be if you worked for the company for 12 years.
Set up a function S(y) where y is the number of years after you start at the Roof and Vinyl place.
S(y) = 45600 * (1.035)^y <-- Since 3.5% = 0.035
The question asks for S(12):
S(12) = 45600 * (1.035)^12
S(12) = 45600 * 1.51106865735
S(12) = [B]68,904.73[/B]

Consecutive Integer Word Problems

Calculates the word problem for what two consecutive integers, if summed up or multiplied together, equal a number entered.

Consider the following 15 numbers 1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20 - The mean o

Consider the following 15 numbers
1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20
- The mean of the last 10 numbers is TWICE the mean of the first 10 numbers
- The sum of the last 2 numbers is FIVE times the sum of the first 3 numbers
(i) Calculate the values of x and y
We're given two equations:
[LIST=1]
[*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = 2(1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/10
[*]3x - 20 = 5(1 + 2 + y - 4)
[/LIST]
Let's evaluate and simplify:
[LIST=1]
[*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = (1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5
[*]3x - 20 = 5(y - 1)
[/LIST]
Simplify some more:
[URL='https://www.mathcelebrity.com/polynomial.php?num=x%2B6%2B7%2B8%2By%2B9%2B10%2B12%2B3x%2B20&pl=Evaluate'](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10[/URL] = (4x + y + 72)/10
[URL='https://www.mathcelebrity.com/polynomial.php?num=1%2B2%2By-4%2B4%2B5%2Bx%2B6%2B7%2B8%2By&pl=Evaluate'](1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5[/URL] = (2y + x + 29)/5
5(y - 1) = 5y - 5
So we're left with:
[LIST=1]
[*](4x + y + 72)/10 = (2y + x + 29)/5
[*]3x - 20 = 5y - 5
[/LIST]
Cross multiply equations in 1, we have:
5(4x + y + 72) = 10(2y + x + 29)
20x + 5y + 360 = 20y + 10x + 290
We have:
[LIST=1]
[*]20x + 5y + 360 = 20y + 10x + 290
[*]3x - 20 = 5y - 5
[/LIST]
Combining like terms:
[LIST=1]
[*]10x - 15y = -70
[*]3x - 5y = 15
[/LIST]
Now we have a system of equations which we can solve any of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
(x, y) = [B](-115, -72)[/B]

Construct a data set of seven temperature readings where the mean is positive and the median is nega

Construct a data set of seven temperature readings where the mean is positive and the median is negative.
[B]{-20,-10.-5,-2,-1,20,40}[/B]
[URL='https://www.mathcelebrity.com/statbasic.php?num1=-20%2C-10%2C-5%2C-2%2C-1%2C20%2C40&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Using our mean and median calculator[/URL], we see that:
[B]Mean = 3.142857 (positive)
Median = -2[/B]

Counting

Counts up from a number to another number using a factor

Counts down from one number to another number using a factor. Also known as skip counting.

Counts down from one number to another number using a factor. Also known as skip counting.

Counting on a Number Line

Shows addition or subtraction by moving left or right on a number line.

Craig went bowling with $25 to spend. He rented shoes for $5.25 and paid $4.00 for each game. What w

Craig went bowling with $25 to spend. He rented shoes for $5.25 and paid $4.00 for each game. What was the greatest number of games Craig could have played?
Set up the cost function C(g) where g is the number of games Craig plays:
C(g) = Game fee * number of games (g) + shoe rental fee
C(g) = 4g + 5.25
The problem asks for the maximum number of games Craig can play for $25. So we want an inequality of [I]less than or equal to[/I].
4g + 5.25 <= 25
[URL='https://www.mathcelebrity.com/1unk.php?num=4g%2B5.25%3C%3D25&pl=Solve']Type this inequality into our search engine[/URL], and we get:
g <= 4.9375
We want exact games, so we round this down to [B]4 games[/B].

cube root of a number and 7

cube root of a number and 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Cube root of a number means we raise x to the 1/3 power:
x^1/3
And 7 means we add 7:
[B]x^1/3 + 7[/B]

D= {a,b,c,d,e,f,g} the cardinality of set D is

D= {a,b,c,d,e,f,g} the cardinality of set D is
Cardinality of D, denoted |D|, is the number of items in the set:
|D| = [B]7[/B]

Dakota needs a total of $400 to buy a new bicycle. He has $40 saved. He earns $15 each week deliveri

Dakota needs a total of $400 to buy a new bicycle. He has $40 saved. He earns $15 each week delivering newspapers. How many weeks will Dakota have to deliver papers to have enough money to buy the bicycle?
Let w be the number of weeks of delivering newspapers. We have the equation:
15w + 40 = 400
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=15w%2B40%3D400&pl=Solve']type this equation into our search engine[/URL] and we get:
w = [B]24[/B]

Dale has a bookcase with d shelves. There are 14 books on each shelf. Using d, write an expression f

Dale has a bookcase with d shelves. There are 14 books on each shelf. Using d, write an expression for the total number of books.
We multiply the number of shelves by the number of books per shelf.
[B]14d[/B]

Dan earns Ł9.80 per hour. How much will he earn for 8 hours work?

Dan earns Ł9.80 per hour. How much will he earn for 8 hours work?
Calculate Total Earnings
Total Earnings = Hourly Rate * Number of Hours
Total Earnings = Ł9.80 * 8
Total Earnings = [B]Ł78.40[/B]

Dan has a favorite fast food restaurant where he always orders French fries and a milk shake. If the

Dan has a favorite fast food restaurant where he always orders French fries and a milk shake. If the fries contain 15 grams of fat and the shake contains 9 grams of fat, how many burgers, at 17 grams of fat each, can Dan add to his fries and milkshake if he wants to keep the total fat content of his meal no greater than 69 grams?
His original meal is 1 fry and 1 shake. This contains 15 + 9 = 24 grams of fat.
To limit his meal to 69 grams of fat, he has 69 - 24 = 45 grams of fat left over.
Therefore, he can consume:
17b <= 45 where b is the number of burgers
Dividing by 17, we get b = 2.65. Since he does not want to go over 45, he can eat 2 burgers.

Dan makes 11 an hour working at the local grocery store. Over the past year he has saved 137.50 towa

Dan makes 11 an hour working at the local grocery store. Over the past year he has saved 137.50 toward a new pair of retro sneakers. If sneakers cost 240, how many hours will he need to be able to buy the sneakers?
Figure out his remaining savings target:
240 - 137.50 = 102.50
Let x equal the number of remaining hours Dan needs to work
11x = 102.50
Divide each side by 11
x = 9.318
We round up for a half-hour to 9.5, or a full hour to 10.

Dan's school is planning a field trip to an art museum. Bus company A charges a $60 rental fee plus

Dan's school is planning a field trip to an art museum. Bus company A charges a $60 rental fee plus $4 per student. Bus company B charges $150 plus $2 per student. How many students would have to go for the cost to be the same?
[U]Set up Company A's cost equation C(s) where s is the number of students[/U]
C(s) = Cost per student * s + Rental Fee
C(s) = 4s + 60
[U]Set up Company B's cost equation C(s) where s is the number of students[/U]
C(s) = Cost per student * s + Rental Fee
C(s) = 2s + 150
The problem asks for s where both C(s) equations would be equal. So we set Company A and Company B's C(s) equal to each other:
4s + 60 = 2s + 150
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B60%3D2s%2B150&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]45[/B]

Dane wrote the letters of “NEW YORK CITY” on cards and placed them in a hat. What is the probability

Dane wrote the letters of “NEW YORK CITY” on cards and placed them in a hat. What is the probability that he will draw the letter “Y” out of the hat?
New York City has 11 letters.
Our probability of drawing a Y is denoted as P(Y):
P(Y) = Number of Y's / Total Letters
P(Y) = [B]2/11[/B]

Daniel pays $10 to get into the parking lot and will pay a fee of $2 per hour his car will be left i

Daniel pays $10 to get into the parking lot and will pay a fee of $2 per hour his car will be left in the parking lot. He ending up paying a total of $23 for parking. How many hours was Daniels car left in the parking lot?
Calculate the amount of fees for hours:
Fees for hours = Total Bill - Entrance fee
Fees for hours = 23 - 10
Fees for hours = 13
Calculate the number of hours Daniel parked:
Number of hours = Fees for hours / Hourly Rate
Number of hours = 13/2
Number of hours = [B]6.5[/B]

Danny buys 5 books at $34 each and pays for them with 10-dollar bills. How many $10 bills did it tak

Danny buys 5 books at $34 each and pays for them with 10-dollar bills. How many $10 bills did it take?
Calculate his total bill:
Total bill = Number of books * cost per book
Total bill = 5 * 34
Total bill = 170
Now calculate the number of 10-dollar bills he used:
10-dollar bills used = Total bill / 10
10-dollar bills used = 170/10
10-dollar bills used = [B]17[/B]

Date Information

This calculator takes a date in mm/dd/yyyy format, and gives the following information about it:

* Weekday

* Day number in the year

* Week number in the year

* Number of days in the month containing that date

* Leap Year (Yes or No)

* Zodiac Sign

* Julian Date

* Weekday

* Day number in the year

* Week number in the year

* Number of days in the month containing that date

* Leap Year (Yes or No)

* Zodiac Sign

* Julian Date

DeAndre is a spelunker (someone who explores caves). One day DeAndre is exploring a cave that has a

DeAndre is a spelunker (someone who explores caves). One day DeAndre is exploring a cave that has a series of ladders going down into the depths. Every ladder is exactly 10 feet tall, and there is no other way to descend or ascend (the other paths in the cave are flat). DeAndre starts at 186 feet in altitude, and reaches a maximum depth of 86 feet in altitude.Write an equation for DeAndre's altitude, using x to represent the number of ladders DeAndre used (hint: a ladder takes DeAndre down in altitude, so the coefficient should be negative).
Set up a function A(x) for altitude, where x is the number of ladders used. Each ladder takes DeAndre down 10 feet, so this would be -10x. And DeAndre starts at 186 feet, so we'd have:
[B]A(x) = 186 - 10x[/B]

Deanna has 5-cent stamps and 10-cent stamps. If she has 100 total stamps, what is the value of the s

Deanna has 5-cent stamps and 10-cent stamps. If she has 100 total stamps, what is the value of the stamps? Call the 5-cent stamps n.
Value of 5-cent stamps
0.05n
Number of 10 cent stamps is:
100 - n
Value is 0.10(100 - n) = 10 - 0.10n
Add them both:
10 - 0.10n + 0.05n
[B]10 - 0.05n[/B]

Debbie baked 32 cookies with 4 scoops of flour. With 10 scoops of flour, how many cookies can Debbie

Debbie baked 32 cookies with 4 scoops of flour. With 10 scoops of flour, how many cookies can Debbie bake?
Set up a proportion of cookies to scoops of flour, where c is the number of cookies per 10 scoops of flour:
32/4 = c/10
[URL='https://www.mathcelebrity.com/prop.php?num1=32&num2=c&den1=4&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
c = [B]80[/B]

Decagonal Number

This calculator determines the nth decagonal number

Decompose Number Pairs

Decomposes a number into number pairs of sums.

Decrease 12 by a number

Decrease 12 by a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take 12 and decrease it by x, meaning we subtract x from 12:
[B]12 - x[/B]

decrease a number by 7 and multiply by 6.

decrease a number by 7 and multiply by 6.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Decrease a number by 7:
x - 7
Multiply by 6
[B]6(x - 7)[/B]

Dedra took a total of 6 pages of notes during 2 hours of class. After attending 3 hours of class, ho

Dedra took a total of 6 pages of notes during 2 hours of class. After attending 3 hours of class, how many total pages of notes will Dedra have in her notebook?
Set up a proportion of pages of notes to hours of class where p equals the number of pages of notes Dedra takes for 3 hours of class:
6/2 = p/3
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=p&den1=2&den2=3&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
p = [B]9[/B]

Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up

Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up her account with a starting amount of $850 and is going to take out $65 per month. When would the two accounts have the same amount of money?
We set up a balance equation B(m) where m is the number of months.
[U]Set up Deon's Balance equation:[/U]
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 650 - 40m
[U]Set up Mai's Balance equation:[/U]
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 850 - 65m
When the two accounts have the same amount of money, we can set both balance equations equal to each other and solve for m:
650 - 40m = 850 - 65m
Solve for [I]m[/I] in the equation 650 - 40m = 850 - 65m
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables -40m and -65m. To do that, we add 65m to both sides
-40m + 650 + 65m = -65m + 850 + 65m
[SIZE=5][B]Step 2: Cancel -65m on the right side:[/B][/SIZE]
25m + 650 = 850
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 650 and 850. To do that, we subtract 650 from both sides
25m + 650 - 650 = 850 - 650
[SIZE=5][B]Step 4: Cancel 650 on the left side:[/B][/SIZE]
25m = 200
[SIZE=5][B]Step 5: Divide each side of the equation by 25[/B][/SIZE]
25m/25 = 200/25
m = [B]8[/B]

Derangements - Subfactorials

Calculates the number of derangements/subfactorial !n.

Derek must choose a 4 digit PIN. Each Digit can be chosen from 0 to 9. Derek does not want to reuse

Derek must choose a 4 digit PIN. Each Digit can be chosen from 0 to 9. Derek does not want to reuse any digits. He also only wants an even number that begins with 5. How many possible PINS could he choose from?
[LIST=1]
[*]First digit must begin with 5. So we have 1 choice
[*]We subtract 1 possible digit from digit 3 to have 8 - 1 = 7 possible digits
[*]This digit can be anything other than 5 and the even number in the next step. So we have 0-9 is 10 digits - 2 = 8 possible digits
[*]Last digit must end in 0, 2, 4, 6, 8 to be even. So we have 5 choices
[/LIST]
Our total choices from digits 1-4 are found by multiplying each possible digit choice:
1 * 7 * 8 * 5 = [B]280 possible PINS[/B]

Determine the formula of the given statement by following the procedures. Choose any number then add

Determine the formula of the given statement by following the procedures. Choose any number then add 2. Multiply your answer to 3 and minus 2
For the phrase [I]choose any number[/I] we can use an arbitrary variable, let's call it x.
Add 2:
x + 2
Multiply your answer to 3:
3(x + 2)
And minus 2 which means we subtract:
[B]3(x + 2) - 2[/B]

Determine whether the random variable is discrete or continuous. In each case, state the possible v

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.
(a) The number of customers arriving at a bank between noon and 1:00 P.M.
(i) The random variable is continuous. The possible values are x >= 0.
(ii) The random variable is discrete. The possible values are x = 0, 1, 2,...
(iii) The random variable is continuous. The possible values are x = 0, 1, 2,...
(iv) The random variable is discrete. The possible values are x >= 0.
(b) The amount of snowfall
(i) The random variable is continuous. The possible values are s = 0, 1, 2,...
(ii) The random variable is discrete. The possible values are s >= 0.
(iii) The random variable is discrete. The possible values are s = 0, 1, 2,...
(iv) The random variable is continuous. The possible values are s >= 0.
[B](a) (ii) The random variable is discrete. The possible values are x = 0, 1, 2,...
Discrete variables are limited in the values they can take between 9 and ?
(b) (iv) The random variable is continuous. The possible values are s >= 0. Snowfall can be a decimal and can vary between 0 and ?[/B]

Deyjiana reads 30 pages in 25 minutes. If she reads 210 pages at this rate, how long will it take he

Deyjiana reads 30 pages in 25 minutes. If she reads 210 pages at this rate, how long will it take her?
Set up a proportion of pages to minutes, were m is the number of minutes it takes to read 210 pages:
30/25 = 210/m
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=30&num2=210&den1=25&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search engine[/URL] and we get:
m = [B]175[/B]

Diana earns $8.50 working as a lifeguard. Write an equation to find Dianas money earned m for any nu

Diana earns $8.50 working as a lifeguard. Write an equation to find Dianas money earned m for any numbers of hours h
Set up the revenue function:
[B]R = 8.5h[/B]

difference between 2 positive numbers is 3 and the sum of their squares is 117

difference between 2 positive numbers is 3 and the sum of their squares is 117
Declare variables for each of the two numbers:
[LIST]
[*]Let the first variable be x
[*]Let the second variable be y
[/LIST]
We're given 2 equations:
[LIST=1]
[*]x - y = 3
[*]x^2 + y^2 = 117
[/LIST]
Rewrite equation (1) in terms of x by adding y to each side:
[LIST=1]
[*]x = y + 3
[*]x^2 + y^2 = 117
[/LIST]
Substitute equation (1) into equation (2) for x:
(y + 3)^2 + y^2 = 117
Evaluate and simplify:
y^2 + 3y + 3y + 9 + y^2 = 117
Combine like terms:
2y^2 + 6y + 9 = 117
Subtract 117 from each side:
2y^2 + 6y + 9 - 117 = 117 - 117
2y^2 + 6y - 108 = 0
This is a quadratic equation:
Solve the quadratic equation 2y2+6y-108 = 0
With the standard form of ax2 + bx + c, we have our a, b, and c values:
a = 2, b = 6, c = -108
Solve the quadratic equation 2y^2 + 6y - 108 = 0
The quadratic formula is denoted below:
y = -b ± sqrt(b^2 - 4ac)/2a
[U]Step 1 - calculate negative b:[/U]
-b = -(6)
-b = -6
[U]Step 2 - calculate the discriminant ?:[/U]
? = b2 - 4ac:
? = 62 - 4 x 2 x -108
? = 36 - -864
? = 900 <--- Discriminant
Since ? is greater than zero, we can expect two real and unequal roots.
[U]Step 3 - take the square root of the discriminant ?:[/U]
?? = ?(900)
?? = 30
[U]Step 4 - find numerator 1 which is -b + the square root of the Discriminant:[/U]
Numerator 1 = -b + ??
Numerator 1 = -6 + 30
Numerator 1 = 24
[U]Step 5 - find numerator 2 which is -b - the square root of the Discriminant:[/U]
Numerator 2 = -b - ??
Numerator 2 = -6 - 30
Numerator 2 = -36
[U]Step 6 - calculate your denominator which is 2a:[/U]
Denominator = 2 * a
Denominator = 2 * 2
Denominator = 4
[U]Step 7 - you have everything you need to solve. Find solutions:[/U]
Solution 1 = Numerator 1/Denominator
Solution 1 = 24/4
Solution 1 = 6
Solution 2 = Numerator 2/Denominator
Solution 2 = -36/4
Solution 2 = -9
[U]As a solution set, our answers would be:[/U]
(Solution 1, Solution 2) = (6, -9)
Since one of the solutions is not positive and the problem asks for 2 positive number, this problem has no solution

Digit Problems

Determines how many (n) digit numbers can be formed based on a variety of criteria.

Digit Product

Calculates a digit product for a number.

Digit Sum

Calculates a digit sum and reduced digit sum for a number.

distance between -2 and 9 on the number line

distance between -2 and 9 on the number line
Distance on the number line is the absolute value of the difference:
D = |9 - -2|
D = |11|
D = [B]11[/B]

Distributive Property

Demonstrates the distributive property using 3 numbers.
Numerical Properties

Divide a number by 10. Then, add 10.

Divide a number by 10. Then, add 10.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Divide the number by 10 mean we have a quotient, of x over 10
x / 10
Then, add 10:
[B](x / 10) + 10[/B]

Divisibility

Shows the divisibility of a number by seeing if it is divisible by (2,3,4,5,6,7,8,9,10,11)

Divya has 70 rocks. She donates half of the rocks to a science center. Then she collects 3 rocks on

Divya has 70 rocks. She donates half of the rocks to a science center. Then she collects 3 rocks on each of her nature hikes. Write an expression to represent the number of rocks Divya has after she collects rocks on n nature hikes.
For each hike, we have:
[LIST=1]
[*]Start with 70 rocks
[*]She donates half which is 35, which means she's left with 35
[/LIST]
Since each nature hike gives her 3 more rocks, and she goes on n nature hikes, we have the following algebraic expression:
[B]3n + 35[/B]

Do the phrases 7 less than a number and a number less than 7 mean the same thing explain

Do the phrases 7 less than a number and a number less than 7 mean the same thing explain
No, they are different, here's how:
First, the phrase [I]a number[/I] means an arbitrary variable, let's call it x.
7 less than a number means we subtract 7 from x:
x - 7
A number less than 7 means we subtract x from 7:
7 - x
As you can see:
x - 7 <> 7 - x so [B]they are different[/B]

Dora has $35 saved. She earns $9.50 per hour at her job. How many hours must she work to have a tota

Dora has $35 saved. She earns $9.50 per hour at her job. How many hours must she work to have a total of $358 in her savings?
Subtract the existing savings from the desired savings to see what we have left:
358 - 35 = 323
Now, at 9.50 per hour, how many hours of work does she need to get 323?
Let h be the number of hours. We have:
9.50h = 323
[URL='http://www.mathcelebrity.com/1unk.php?num=9.50h%3D323&pl=Solve']Running this problem through our search engine[/URL], we get
[B]h = 34[/B]

Dotty McGinnis starts up a small business manufacturing bobble-head figures of famous soccer players

Dotty McGinnis starts up a small business manufacturing bobble-head figures of famous soccer players. Her initial cost is $3300. Each figure costs $4.50 to make. a. Write a cost function, C(x), where x represents the number of figures manufactured.
Cost function is the fixed cost plus units * variable cost.
[B]C(x) = 3300 + 4.50x[/B]

Dr. Carlson is contemplating the impact of an antibiotic on a particular patient. The patient will t

Dr. Carlson is contemplating the impact of an antibiotic on a particular patient. The patient will take 229 milligrams, and every hour his body will break down 20% of it. How much will be left after 9 hours?
Set up the antibiotic remaining function A(h) where h is the number of hours after the patient takes the antibiotic.
If the body breaks down 20%, then the remaining is 100% - 20% = 80%
80% as a decimal is 0.8, so we have:
A(h) = 229 * (0.8)^h
The problems asks for A(9):
A(9) = 229 * (0.8)^9
A(9) = 229 * 0.134217728
A(9) = [B]30.74 milligrams[/B]

Dr. Hoffman is contemplating the impact of an antibiotic on a particular patient. The patient will t

Dr. Hoffman is contemplating the impact of an antibiotic on a particular patient. The patient will take 590 milligrams, and every hour his body will break down 30% of it. How much will be left after 8 hours? If necessary, round your answer to the nearest tenth.
Set up a function A(h), where h is the number of hours since the patient took the antibiotic.
If the body breaks down 30%, it keeps 70%, or 0.7.
A(h) = 590(0.70)^h
The problem asks for A(8):
A(8) = 590(0.70)^8
A(8) =590 * 0.05764801
A(8) = 34.012 hours
Rounded to the nearest tenth, it's [B]34.0 hours[/B].

Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers

Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers business cards for $0.15 each with a setup charge of $10. What numbers of business cards cost the same from either company
Declare variables:
[LIST]
[*]Let b be the number of business cards.
[/LIST]
[U]Set up the cost function C(b) for Dunder Mifflin:[/U]
C(b) = Cost to print each business card * b + Setup Charge
C(b) = 0.1b + 15
[U]Set up the cost function C(b) for Werham Hogg:[/U]
C(b) = Cost to print each business card * b + Setup Charge
C(b) = 0.15b + 10
The phrase [I]cost the same[/I] means we set both C(b)'s equal to each other and solve for b:
0.1b + 15 = 0.15b + 10
Solve for [I]b[/I] in the equation 0.1b + 15 = 0.15b + 10
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 0.1b and 0.15b. To do that, we subtract 0.15b from both sides
0.1b + 15 - 0.15b = 0.15b + 10 - 0.15b
[SIZE=5][B]Step 2: Cancel 0.15b on the right side:[/B][/SIZE]
-0.05b + 15 = 10
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 15 and 10. To do that, we subtract 15 from both sides
-0.05b + 15 - 15 = 10 - 15
[SIZE=5][B]Step 4: Cancel 15 on the left side:[/B][/SIZE]
-0.05b = -5
[SIZE=5][B]Step 5: Divide each side of the equation by -0.05[/B][/SIZE]
-0.05b/-0.05 = -5/-0.05
b = [B]100[/B]

Duplication and Mediation

Multiplies two numbers using Duplication and Mediation

During the 2016 christmas season,UPS had 14 employees retire, 122 employees were hired and 31 left d

During the 2016 christmas season,UPS had 14 employees retire, 122 employees were hired and 31 left due to illness. If UPS ended the year with 410 employees, how many did they have at the start of the season?
Let x be the number of employees at the start of the season. We have:
[LIST]
[*]-14 since retiring is an employee loss
[*]+122 hired since hiring is an employee gain
[*]-31 since illness means a leave
[/LIST]
x - 14 + 122 - 31 = 410
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=x-14%2B122-31%3D410&pl=Solve']equation solver[/URL], we get:
[B]x = 333[/B]

Dylan is playing darts. He hit the bullseye on 5 out of his last 20 tosses. Considering this data, h

Dylan is playing darts. He hit the bullseye on 5 out of his last 20 tosses. Considering this data, how many bullseyes would you expect Dylan to get during his next 16 tosses?
We have a proportion of bullseyes to tosses where b is the number of bullseyes for 16 tosses:
5/20 = b/16
[URL='https://www.mathcelebrity.com/prop.php?num1=5&num2=b&den1=20&den2=16&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get:
b = [B]4[/B]

Dylans mother tells Dylan he must spend less time playing electronic games. On the weekends he spend

Dylans mother tells Dylan he must spend less time playing electronic games. On the weekends he spends 9.5 hours playing electronic games. If he plays between 13 and 19 hours each week, how many hours does he play games on weekdays?
Let x equal the number of hours Dylan plays electronic games per week.
[U]Set up our inequality:[/U]
13 <= x <= 19
[U]To see how much he plays during weekdays, subtract off the weekend time[/U]
13 - 9.5 <= x <= 19 - 9.5
[B]3.5 <= x <= 9.5[/B]

Each brick is 14 inches long, 8 inches wide, and 5 inches tall.if they used 16,800 in3 of concrete,

Each brick is 14 inches long, 8 inches wide, and 5 inches tall.if they used 16,800 in3 of concrete, how many bricks did they make?
Volume of a brick (V) is:
V = l * w * h
Plugging in our brick measurements, we get:
V = 14 * 8 * 5
V = 560
Calculate number of bricks:
Number of Bricks = Total Volume / Volume of one Brick
Number of Bricks = 16,800/560
Number of Bricks =[B]30[/B]

Each class can have 40 pupils. If a school opens 5 classes for Grade 6, how many Grade 6 pupils can

Each class can have 40 pupils. If a school opens 5 classes for Grade 6, how many Grade 6 pupils can it accept?
Grade 6 pupils = pupils per class * number of classes
Grade 6 pupils = 40 * 5
Grade 6 pupils = [B]200 pupils[/B]

each classroom at HCS has a total of 26 desks. After Mr. Sean pond ordered 75 new desks the total nu

each classroom at HCS has a total of 26 desks. After Mr. Sean pond ordered 75 new desks the total number of desks in the school was 543. How many classrooms does the school have?
Let d be the number of desks per classroom. We're given an equation:
26d + 75 = 543
To solve for d, [URL='https://www.mathcelebrity.com/1unk.php?num=26d%2B75%3D543&pl=Solve']type this equation into our search engine[/URL] and we get:
d = [B]18[/B]

Each of 6 students reported the number of movies they saw in the past year. Here is what they repor

Each of 6 students reported the number of movies they saw in the past year. Here is what they reported. 19, 9, 14, 10, 16, 17. Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth.
The mean is the average, so we add up the 6 movie scores, and divide by 6.
[URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = Sum of 6 Movie Scores / 6
[URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = 84 / 6
[URL='https://www.mathcelebrity.com/statbasic.php?num1=19%2C+9%2C+14%2C+10%2C+16%2C+17&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']Mean (Average)[/URL] = 14.16666667
The problem asks us to round to the nearest tenth, which is the first decimal place.
Since the 2nd decimal place, 6 is more than 5, we round the first decimal place up one and remove the rest.
[B]14.2[/B]

Each tree in an orchard containing 2,650 trees requires 210 grams of fertiliizer. At $1.25 per kilog

Each tree in an orchard containing 2,650 trees requires 210 grams of fertiliizer. At $1.25 per kilogram of fertilizer, how much does it cost to fertilize the orchard?
[U]Calculate the total fertilizer needed:[/U]
Total fertilizer needed = Number of trees * grams of fertilizer per tree
Total fertilizer needed = 2650 * 210
[URL='https://www.mathcelebrity.com/longdiv.php?num1=2650&num2=210&pl=Multiply']Total fertilizer needed[/URL] = 556500 grams
[U]1 kilogram = 1000 grams, so we convert our 556500 grams to kilograms:[/U]
kilograms of fertilizer = grams of fertilizer / 1000
kilograms of fertilizer = 556500/1000
kilograms of fertilizer = 556.5
[U]Calculate fertilizer cost:[/U]
Fertilizer cost = kilograms of fertilizer * cost per kilogram
Fertilizer cost = 556.5 * 1.25
Fertilizer cost = [B]695.63[/B]

Eight less then the sum of y and x

The sum of y and x is denoted as:
x + y
Eight less than that, using the number (8) for eight is:
x + y - 8

Eight students made 272.00 mowing lawns. How much did each student make?

Eight students made 272.00 mowing lawns. How much did each student make?
Earnings per Student = Total Earnings / Number of Students
Earnings per Student = 272/8
Earnings per Student = [B]34[/B]

Elsa took a total of 25 quizzes over the course of 5 weeks. After attending 8 weeks of school this q

Elsa took a total of 25 quizzes over the course of 5 weeks. After attending 8 weeks of school this quarter, how many quizzes will Elsa have taken in total? Assume the relationship is directly proportional.
Set up a proportion of quizzes to weeks where q is the number of quizzes taken in 8 weeks. We have:
25/5 = q/8
We [URL='https://www.mathcelebrity.com/prop.php?num1=25&num2=q&den1=5&den2=8&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search engine[/URL] and we get:
q = [B]40[/B]

entry at a zoo costs $30 for an adult and $25 for a child. How much would it cost for 2 adults and 3

entry at a zoo costs $30 for an adult and $25 for a child. How much would it cost for 2 adults and 3 children?
Cost = Price * Quantity, so we have:
Cost = Price per adult * number of adults + Price per child * number of children
Cost = 30 * 2 + 25 * 3
Cost = 60 + 75
Cost = [B]135[/B]

Erica has $14 and plans to save $5 each week until she has the $64 she needs for a new jacket. Par

Erica has $14 and plans to save $5 each week until she has the $64 she needs for a new jacket. Part A: Write a number sentence describing this situation, using W to stand for the number of weeks Erica needs to save.
[B]14 + 5w = 64[/B]

Erik is rolling two regular six-sided number cubes. What is the probability that he will roll an eve

Erik is rolling two regular six-sided number cubes. What is the probability that he will roll an even number on one cube and a prime number on the other?
P(Even on first cube) = (2,4,6) / 6 total choices
P(Even on first cube) = 3/6
P(Even on first cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL]
P(Prime on second cube) = (2,3,5) / 6 total choices
P(Prime on second cube) = 3/6
P(Prime on second cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL]
Since each event is independent, we have:
P(Even on the first cube, Prime on the second cube) = P(Even on the first cube) * P(Prime on the second cube)
P(Even on the first cube, Prime on the second cube) = 1/2 * 1/2
P(Even on the first cube, Prime on the second cube) = [B]1/4[/B]

Erin has 72 stamps in her stamp drawer along with a quarter, two dimes and seven pennies. She has 3

Erin has 72 stamps in her stamp drawer along with a quarter, two dimes and seven pennies. She has 3 times as many 3-cent stamps as 37-cent stamps and half the number of 5-cent stamps as 37-cent stamps. The value of the stamps and coins is $8.28. How many 37-cent stamps does Erin have?
Number of stamps:
[LIST]
[*]Number of 37 cent stamps = s
[*]Number of 3-cent stamps = 3s
[*]Number of 5-cent stamps = 0.5s
[/LIST]
Value of stamps and coins:
[LIST]
[*]37 cent stamps = 0.37s
[*]3-cent stamps = 3 * 0.03 = 0.09s
[*]5-cent stamps = 0.5 * 0.05s = 0.025s
[*]Quarter, 2 dime, 7 pennies = 0.52
[/LIST]
Add them up:
0.37s + 0.09s + 0.025s + 0.52 = 8.28
Solve for [I]s[/I] in the equation 0.37s + 0.09s + 0.025s + 0.52 = 8.28
[SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE]
(0.37 + 0.09 + 0.025)s = 0.485s
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
0.485s + 0.52 = + 8.28
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 0.52 and 8.28. To do that, we subtract 0.52 from both sides
0.485s + 0.52 - 0.52 = 8.28 - 0.52
[SIZE=5][B]Step 4: Cancel 0.52 on the left side:[/B][/SIZE]
0.485s = 7.76
[SIZE=5][B]Step 5: Divide each side of the equation by 0.485[/B][/SIZE]
0.485s/0.485 = 7.76/0.485
s = [B]16[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.37s%2B0.09s%2B0.025s%2B0.52%3D8.28&pl=Solve']Source[/URL]

Estimate Square Roots

Estimates the square root of a number

Estimate Sums

Estimates the sum of 2 numbers.

Estimating Reasonableness of Products

Given a product of 2 numbers and an estimated product, this will check to see if it is reasonable

Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, wh

Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, whereas Kurt is contributing $1 per day. Eventually, the two accounts will contain the same amount. What balance will each account have? How long will that take?
Set up account equations A(d) where d is the number of days since time 0 for each account.
Ethan A(d): 9079 + 19d
Kurt A(d): 9259 + d
The problems asks for when they are equal, and how much money they have in them. So set each account equation equal to each other:
9079 + 19d = 9259 + d
[URL='https://www.mathcelebrity.com/1unk.php?num=9079%2B19d%3D9259%2Bd&pl=Solve']Typing this equation into our search engine[/URL], we get [B]d = 10[/B].
So in 10 days, both accounts will have equal amounts in them.
Now, pick one of the account equations, either Ethan or Kurt, and plug in d = 10. Let's choose Kurt's since we have a simpler equation:
A(10) = 9259 + 10
A(10) = $[B]9,269
[/B]
After 10 days, both accounts have $9,269 in them.

Euclids Algorithm and Euclids Extended Algorithm

Given 2 numbers a and b, this calculates the following

1) The Greatest Common Divisor (GCD) using Euclids Algorithm

2) x and y in Bézouts Identity ax + by = d using Euclids Extended Algorithm Extended Euclidean Algorithm

1) The Greatest Common Divisor (GCD) using Euclids Algorithm

2) x and y in Bézouts Identity ax + by = d using Euclids Extended Algorithm Extended Euclidean Algorithm

Eva earns $72 washing 6 cars. At this rate, how many cars did Eva wash to earn $132?

Eva earns $72 washing 6 cars. At this rate, how many cars did Eva wash to earn $132?
Set up a proportion of money to cars washed where c is the number of cars washed for $132 in earnings:
72/6 = 132/c
[URL='https://www.mathcelebrity.com/prop.php?num1=72&num2=132&den1=6&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our calculator[/URL], we get:
[B]c = 11[/B]

evaluate 16 raised to 1/4

evaluate 16 raised to 1/4
What number raised to the 4th power equals 16?
[B]2[/B], since 2 * 2 * 2 * 2 = 16

evelyn needs atleast $112 to buy a new dress. She has already saved $40 . She earns $9 an hour babys

evelyn needs atleast $112 to buy a new dress. She has already saved $40 . She earns $9 an hour babysitting. How many hours will she need to babysit to buy the dress?
Let the number of hours be h.
We have the earnings function E(h) below
E(h) = hourly rate * h + current savings
E(h) = 9h + 40
We're told E(h) = 112, so we have:
9h + 40 = 112
[URL='https://www.mathcelebrity.com/1unk.php?num=9h%2B40%3D112&pl=Solve']Typing this equation in our math engine[/URL] and we get:
h = [B]8[/B]

Even Numbers

Shows a set amount of even numbers and cumulative sum

Every 100 seeds of corn he plants, he harvests 84 ears of corn. If he wants to harvest 7200 ears of

Every 100 seeds of corn he plants, he harvests 84 ears of corn. If he wants to harvest 7200 ears of corn, how many seeds must he plant?
Set up a proportion seeds to ears:
100/84 = x/7200 where x is the number of seeds needed for 7200 ears of corn.
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=100&num2=x&den1=84&den2=7200&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
[B]x = 8,571.43 ~ 8,572[/B]

Expanded Notation

Writes the expanded notation for a number.

Explain the relationship between "squaring" a number and finding the "square root" of a number. Use

Explain the relationship between "squaring" a number and finding the "square root" of a number. Use an example to further explain your answer.
Squaring a number means raising it to the power of 2
The square root of a number [I]undoes[/I] a square of a number.
So square root of x^2 is x
x squared is x^2
Let x = 5.
x squared = 5^2 = 25
Square root of 25 = square root of 5^2 = 5

Explain why 1/2 and 3/6 are equivalent

Explain why 1/2 and 3/6 are equivalent.
Multiply any number by 1, and we get the same number.
Multiply 1/2 by 3/3 which is 1
(1 * 3)/(2 *3) = 3/6

Factorials

Calculates the following factorial items:

* A factorial of one number such as n!

* A factorial of a numerator divided by a factorial of a denominator such as n!m!/a!b!

* Double Factorials such as n!!

* Stirlings Approximation for n!

* A factorial of one number such as n!

* A factorial of a numerator divided by a factorial of a denominator such as n!m!/a!b!

* Double Factorials such as n!!

* Stirlings Approximation for n!

Factoring and Root Finding

This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential*positive* and *negative* roots using Descarte’s Rule of Signs

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential

Factorization

Given a positive integer, this calculates the following for that number:

1) Factor pairs and prime factorization and prime power decomposition

2) Factors and Proper Factors 3) Aliquot Sum

1) Factor pairs and prime factorization and prime power decomposition

2) Factors and Proper Factors 3) Aliquot Sum

Farmer Bob can get 10 gallons of milk from 4 cows. How many gallons of milk can he get from 14 cows?

Farmer Bob can get 10 gallons of milk from 4 cows. How many gallons of milk can he get from 14 cows?
Set up a proportion of gallons to cows where g is the number of gallons per 14 cows:
10/4 = g/14
To solve this proportion for g, we[URL='https://www.mathcelebrity.com/prop.php?num1=10&num2=g&den1=4&den2=14&propsign=%3D&pl=Calculate+missing+proportion+value'] type it in our search engine[/URL] and we get:
g = [B]35
[/B]

Farmer Yumi has too many plants in her garden. If she starts out with 150 plants and is losing them

Farmer Yumi has too many plants in her garden. If she starts out with 150 plants and is losing them at a rate of 4% each day, how long will it take for her to have 20 plants left? Round UP to the nearest day.
We set up the function P(d) where d is the number of days sine she started losing plants:
P(d) = Initial plants * (1 - Loss percent / 100)^d
Plugging in our numbers, we get:
20 = 150 * (1 - 4/100)^d
20 = 150 * (1 - 0.04)^d
Read left to right so it's easier to read:
150 * 0.96^d = 20
Divide each side by 150, and we get:
0.96^d = 0.13333333333
To solve this logarithmic equation for d, we [URL='https://www.mathcelebrity.com/natlog.php?num=0.96%5Ed%3D0.13333333333&pl=Calculate']type it in our search engine[/URL] and we get:
d = 49.35
The problem tells us to round up, so we round up to [B]50 days[/B]

Fermats Little Theorem

For any integer a and a prime number p, this demonstrates Fermats Little Theorem.

Fibonacci Sequence

Generates a list of the first 100 Fibonacci numbers.
Also shows how to generate the nth Fibonacci number using Binet's Formula

Fifteen less than 3

Convert to numbers:
Fifteen = 15.
Less than means subtract.
3 - 15.
Evaluating, that is 12.

Fifty-two less than 75% of a number

Fifty-two less than 75% of a number
A number means an arbitrary variable, let's call it x.
75% of this is 0.75x
Fifty-two less is:
[B]0.75x - 52[/B]

Finance

1. Spend 8000 on a new machine. You think it will provide after tax cash inflows of 3500 per year for the next three years. The cost of funds is 8%. Find the NPV, IRR, and MIRR. Should you buy it?
2. Let the machine in number one be Machine A. An alternative is Machine B. It costs 8000 and will provide after tax cash inflows of 5000 per year for 2 years. It has the same risk as A. Should you buy A or B?
3. Spend 100000 on Machine C. You will need 5000 more in net working capital. C is three year MACRS. The cost of funds is 8% and the tax rate is 40%. C is expected to increase revenues by 45000 and costs by 7000 for each of the next three years. You think you can sell C for 10000 at the end of the three year period.
a. Find the year zero cash flow.
b. Find the depreciation for each year on the machine.
c. Find the depreciation tax shield for the three operating years.
d. What is the projects contribution to operations each year, ignoring depreciation effects?
e. What is the cash flow effect of selling the machine?
f. Find the total CF for each year.
g. Should you buy it?

Find 2 consecutive numbers such that the sum of twice the smaller number and 3 times the larger numb

Find 2 consecutive numbers such that the sum of twice the smaller number and 3 times the larger number is 73.
Let x be the smaller number and y be the larger number. We are given:
2x + 3y = 73
Since the numbers are consecutive, we know that y = x + 1. Substitute this into our given equation:
2x + 3(x + 1) = 73
Multiply through:
2x + 3x + 3 = 73
Group like terms:
5x + 3 = 73
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3%3D73&pl=Solve']Type 5x + 3 = 73 into the search engine[/URL], and we get [B]x = 14[/B].
Our larger number is 14 + 1 = [B]15
[/B]
Therefore, our consecutive numbers are[B] (14, 15)[/B]

Find all numbers whose absolute value is -3

Find all numbers whose absolute value is -3
[B][U][I]None[/I][/U][/B]. Absolute values are always positive, so no number has a negative absolute value.

Find all numbers whose absolute value is 6

Find all numbers whose absolute value is 6.
2 numbers:
|6| = 6
|-6| = 6

find all numbers whose absolute value is 7

find all numbers whose absolute value is 7
|7| = 7
|-7| = 7
So we have two numbers: [B](-7, 7)[/B]

Find all numbers who’s absolute value is 7

Find all numbers who’s absolute value is 7
We have 2 numbers with an absolute value of 7:
[LIST=1]
[*][B]7 [/B]since |7| = 7
[*][B]-7[/B] since |-7| = 7
[/LIST]

Find four consecutive odd numbers which add to 64

Find four consecutive odd numbers which add to 64.
Let the first number be x. The next three numbers are:
x + 2
x + 4
x + 6
Add them together to get 64:
x + (x + 2) + (x + 4) + (x + 6) = 64
Group like terms:
4x + 12 = 64
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=4x%2B12%3D64&pl=Solve']equation calculator[/URL], we get:
[B]x = 13[/B]
The next 3 odd numbers are:
x + 2 = 13 + 2 = 15
x + 4 = 13 + 4 = 17
x + 6 = 13 + 6 = 19
So the 4 consecutive odd numbers which add to 64 are:
[B](13, 15, 17, 19)[/B]

Find Requested Value

Using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=5.2%2C4.9%2C2.9%2C5.3%2C3.0%2C4.0%2C5.2%2C5.2%2C3.2%2C4.7%2C3.2%2C3.5%2C4.8%2C4.0%2C5.1&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']statistics number set calculator[/URL], we get a mean of [B]4.28[/B]

find the difference between a mountain with an altitude of 1,684 feet above sea level and a valley

find the difference between a mountain with an altitude of 1,684 feet above sea level and a valley 216 feet below sea level.
Below sea level is the same as being on the opposite side of zero on the number line. To get the difference, we do the following:
1,684 - (-216)
Since subtracting a negative is a positive, we have:
1,684 + 216
[B]1,900 feet[/B]

Find the greatest number which divides 845 and 1250

Find the greatest number which divides 845 and 1250
This is the greatest common factor. We [URL='https://www.mathcelebrity.com/gcflcm.php?num1=845&num2=1250&num3=&pl=GCF+and+LCM']type GCF(845,1250) into our search engine [/URL]and we get:
[B]5[/B]

Find the number of combinations and the number of permutations for 10 objects taken 6 at a time

Find the number of combinations and the number of permutations for 10 objects taken 6 at a time
[LIST]
[*]Combinations is written as 10 C 6. Using our [URL='http://www.mathcelebrity.com/permutation.php?num=10&den=6&pl=Combinations']combinations calculator[/URL], we get [B]210[/B].
[*]Permutations is written as 10 P 6. Using our [URL='http://www.mathcelebrity.com/permutation.php?num=10&den=6&pl=Permutations']permutations calculator[/URL], we get [B]151,200[/B].
[/LIST]

Find the odd number less than 100 that is divisible by 9, and when divided by 10 has a remainder of

Find the odd number less than 100 that is divisible by 9, and when divided by 10 has a remainder of 7.
From our [URL='http://www.mathcelebrity.com/divisibility.php?num=120&pl=Divisibility']divisibility calculator[/URL], we see a number is divisible by 9 if the sum of its digits is divisible by 9.
Starting from 1 to 99, we find all numbers with a digit sum of 9.
This would be digits with 0 and 9, 1 and 8, 2 and 7, 3 and 6, and 4 and 5.
9
18
27
36
45
54
63
72
81
90
Now remove even numbers since the problem asks for odd numbers
9
27
45
63
81
Now, divide each number by 10, and find the remainder
9/10 = 0
[URL='http://www.mathcelebrity.com/modulus.php?num=27mod10&pl=Calculate+Modulus']27/10[/URL] = 2 R 7
We stop here. [B]27[/B] is an odd number, less than 100, with a remainder of 7 when divided by 10.

Find the total coast of four nights lodging at $62.00 per night with 8 1/2% sales tax.

Find the total coast of four nights lodging at $62.00 per night with 8 1/2% sales tax.
[U]Calculate Total lodging cost[/U]
Total lodging cost = Nightly Rate * Number of Nights
Total lodging cost = 62 * 4
Total lodging cost = 248
[U]Calculate total bill with tax[/U]
Total bill with tax = Total bill * (1 + sales tax percent)
Total bill with tax = 248 * (1 + 0.85) <-- 8 1/2% = 0.085 as a decimal
Total bill with tax = 248 * 1.085
Total bill with tax =[B] $269.08[/B]

Find two numbers word problems

Given two numbers with a sum of s where one number is n greater than another, this calculator determines both numbers.

Fiona thinks of a number. fiona halves the number and gets an answer of 72.8. Form an equation with

Fiona thinks of a number. fiona halves the number and gets an answer of 72.8. Form an equation with x from the information
Halving means dividing by 2, so our equation is:
[B]x/2 = 72.8[/B]

Five less than a number is at least -7 and at most 7.

Five less than a number is at least -7 and at most 7.
A number signifies an arbitrary variable, let's call it x.
Five less than a number: x - 5
Is at least -7 means greater than or equal to and at most 7 means less than or equal to, so we have a joint inequality:
[B]-7 <= x - 5 <= 7[/B]

Fixed cost 500 marginal cost 8 item sells for 30

fixed cost 500 marginal cost 8 item sells for 30.
Set up Cost Function C(x) where x is the number of items sold:
C(x) = Marginal Cost * x + Fixed Cost
C(x) = 8x + 500
Set up Revenue Function R(x) where x is the number of items sold:
R(x) = Revenue per item * items sold
R(x) = 30x
Set up break even function (Cost Equals Revenue)
C(x) = R(x)
8x + 500 = 30x
Subtract 8x from each side:
22x = 500
Divide each side by 22:
x = 22.727272 ~ 23 units for breakeven

Flight is $295 and car rental is $39 a day, if a competition charges $320 and $33 a day car rental,

Flight is $295 and car rental is $39 a day, if a competition charges $320 and $33 a day car rental, which is cheaper?
Set up cost function where d is the number of days:
[LIST]
[*]Control business: C(d) = 39d + 295
[*]Competitor business: C(d) = 33d + 320
[/LIST]
Set the [URL='http://www.mathcelebrity.com/1unk.php?num=39d%2B295%3D33d%2B320&pl=Solve']cost functions equal to each other[/URL]:
We get d = 4.1667.
The next integer day up is 5. Now plug in d = 1, 2, 3, 4. For the first 4 days, the control business is cheaper. However, starting at day 5, the competitor business is now cheaper forever.

Floor

Determines the floor of a number

for every 10 white cars a dealer sells he sells 7 silver, 6 blue, 5 red, 4 yellow, 3 green, 2 black,

for every 10 white cars a dealer sells he sells 7 silver, 6 blue, 5 red, 4 yellow, 3 green, 2 black, 2 purple and 1 brown car. If he sells 120 cars how many blue cars?
[U]Take this in blocks, so each block has:[/U]
10 white + 7 silver + 6 blue + 5 red + 4 yellow + 3 green + 2 black + 2 purple + 1 brown = 40 cars
[U]Calculate the number of blocks:[/U]
120 cars / 40 cars = 3 blocks.
[U]For 120 cars sold, it takes 3 blocks, which means we multiply:[/U]
6 blue cars per block * 3 blocks = [B]18 blue cars[/B]

For her phone service, Maya pays a monthly fee of $27 , and she pays an additional $0.04 per minu

For her phone service, Maya pays a monthly fee of $27 , and she pays an additional $0.04 per minute of use. The least she has been charged in a month is $86.04 . What are the possible numbers of minutes she has used her phone in a month? Use m for the number of minutes, and solve your inequality for m .
Maya's cost function is C(m), where m is the number of minutes used.
C(m) = 0.04m + 27
We are given C(m) = $86.04. We want her cost function [I]less than or equal[/I] to this.
0.04m + 27 <= 86.04
[URL='https://www.mathcelebrity.com/1unk.php?num=0.04m%2B27%3C%3D86.04&pl=Solve']Type this inequality into our search engine[/URL], and we get [B]m <= 1476[/B].

For the first 10 seconds of the ride, the height of the coaster can be determined by h(t) = 0.3t^3 -

For the first 10 seconds of the ride, the height of the coaster can be determined by h(t) = 0.3t^3 - 5t^2 + 21t, where t is the time in seconds and h is the height in feet. classify this polynomial by degree and by number of terms.
[URL='http://www.mathcelebrity.com/polynomial.php?num=0.3t%5E3-5t%5E2%2B21t&pl=Evaluate']Using our polynomial calculator, we determine[/URL]:
[LIST]
[*]The degree of the polynomial is 3
[*]There are 3 terms
[/LIST]

Foster is centering a photo that is 9/1/2 inches wide on a scrapbook pages that is 10 inches wide. H

Foster is centering a photo that is 9/1/2 inches wide on a scrapbook pages that is 10 inches wide. How far from each side of the pages should he put the picture? Enter your answer as a mixed number.
First, determine your margins, which is the difference between the width and photo width, divided by 2.
10 - 9 & 1/2 = 1/2
1/2 / 2 = [B]1/4[/B]

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?
So the last cousin is n years old. this means consecutive cousins are n + 2 years older than the next.
whether their ages are even or odd, we have the sum of 4 consecutive (odd|even) integers equal to 36. We [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof4consecutiveevenintegersis36&pl=Calculate']type this into our search engine[/URL] and we get the ages of:
[B]6, 8, 10, 12[/B]

Four more then double a number is greater than 2

Four more then double a number is greater than 2
Double a number:
A number implies an arbitrary variable, let's call it "x". Double means multiply this by 2
2x
Four more than this:
2x + 4
Now, we set this expression as an inequality greater than 2
[B]2x + 4 > 2[/B]

Fractions and Mixed Numbers

Given (improper fractions, proper fraction, mixed numbers, or whole numbers), this performs the following operations:

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

Frank is a plumber who charges a $35 service charge and $15 per hour for his plumbing services. Find

Frank is a plumber who charges a $35 service charge and $15 per hour for his plumbing services. Find a linear function that expresses the total cost C for plumbing services for h hours.
Cost functions include a flat rate and a variable rate. The flat rate is $35 and the variable rate per hour is 15. The cost function C(h) where h is the number of hours Frank works is:
[B]C(h) = 15h + 35[/B]

From a regular deck of 52 playing cards, you turn over a 6 and then a 7. What is the probability tha

From a regular deck of 52 playing cards, you turn over a 6 and then a 7. What is the probability that the next card you turn over will be a face card?
Key phrases: 52 card standard deck so you know there's no tricks or missing cards.
[U]Calculate the number of face cards in a standard 52 card deck[/U]
First, we know that face cards = (J, K, Q)
We also know that there are 4 suits (Hearts, Diamonds, Spades, Clubs)
Total Face Cards = 3 face card types * 4 possible suits = 12 face cards
[U]Calculate total face down cards[/U]
First card, you turn over a 6
Next card, you turn over a 7
This means, we have 52 cards - 2 cards from the draws = 50 cards left in the deck which are face down.
P(Face Card) = Total Face Cards / Total Cards in the Deck Face Down
P(Face Card) = 12/50
Simplifying this fraction [URL='https://www.mathcelebrity.com/fraction.php?frac1=12%2F50&frac2=3%2F8&pl=Simplify']using our math engine[/URL], we get:
P(Face Card) = [B]6/25[/B]

Fundamental Rule of Counting

Given a set of items, this calculates the total number of groups/choices that can be formed using the rule of product.

Gabe rents a piano for $49 per month. He earns $15 per hour giving piano lessons to students. How ma

Gabe rents a piano for $49 per month. He earns $15 per hour giving piano lessons to students. How many hours of lessons per month must he give to earn a profit of $326?
Build a profit function P(h) where h is the number of hours:
P(h) = Hourly Rate * Number of Hours (h) - Cost of Piano
P(h) = 15h - 49
The problem asks for the number of hours where P(h) = $326
15h - 49 = 326
We take this equation and [URL='https://www.mathcelebrity.com/1unk.php?num=15h-49%3D326&pl=Solve']type it in our search engine[/URL] to solve for h:
h = [B]25[/B]

Gary is buying chips. Each bag costs $3.50. He has $40 to spend. Write an inequality to represent th

Gary is buying chips. Each bag costs $3.50. He has $40 to spend. Write an inequality to represent the number of chip bags, c, he can afford.
Gary's spend is found by this inequality:
[B]3.50c <= 40
[/B]
To solve this inequality, [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3.50c%3C%3D40&pl=Show+Interval+Notation']we type it in our search engine[/URL] and we get:
[B]c <= 11.43[/B]

Gayle has 36 coins, all nickels and dimes, worth $2.40. How many dimes does she have?

Gayle has 36 coins, all nickels and dimes, worth $2.40. How many dimes does she have?
Set up our given equations using n as the number of nickels and d as the number of dimes:
[LIST=1]
[*]n + d = 36
[*]0.05n + 0.1d = 2.40
[/LIST]
Use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+d+%3D+36&term2=0.05n+%2B+0.1d+%3D+2.40&pl=Cramers+Method']simultaneous equations calculator[/URL] to get:
n = 24
[B]d = 12[/B]

Geocache puzzle help

Let x equal the number of sticks he started with. We have:
The equation is 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) - 0.2 = 19
Add 0.2 to each side:
4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) = 19.2
Multiply each side by 5/4
(3/4 * (2/3 * (0.5x - 0.5) - 1/3) - 0.75) = 24
Multiply the inside piece first:
2/6x - 2/6 - 1/3
2/6x - 4/6
Now subtract 0.75 which is 3/4
2/6x - 4/6 - 3/4
4/6 is 8/12 and 3/4 is 9/12, so we have:
2/6x - 17/12
Now multiply by 3/4
6/24x - 51/48 = 24
Simplify:
1/4x - 17/16 = 24
Multiply through by 4
x - 17/4 = 96
Since 17/4 = 4.25, add 4.25 to each side
x = 100.25
Since he did not cut up any sticks, he has a full stick to start with:
So x = [B]101[/B]

Geocache puzzle help

Let x equal the number of sticks he started with. We have:
The equation is 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) - 0.2 = 19
Add 0.2 to each side:
4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) = 19.2
Multiply each side by 5/4
(3/4 * (2/3 * (0.5x - 0.5) - 1/3) - 0.75) = 24
Multiply the inside piece first:
2/6x - 2/6 - 1/3
2/6x - 4/6
Now subtract 0.75 which is 3/4
2/6x - 4/6 - 3/4
4/6 is 8/12 and 3/4 is 9/12, so we have:
2/6x - 17/12
Now multiply by 3/4
6/24x - 51/48 = 24
Simplify:
1/4x - 17/16 = 24
Multiply through by 4
x - 17/4 = 96
Since 17/4 = 4.25, add 4.25 to each side
x = 100.25
Since he did not cut up any sticks, he has a full stick to start with:
So x = [B]101[/B]

Geometric Distribution

Using a geometric distribution, it calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

Calculates moment number t using the moment generating function

George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a t

George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a total of 25 apples.
Let George's apples be g. Let Sarah's apples be s. We're give two equations:
[LIST=1]
[*]s = 4g
[*]g + s = 25
[/LIST]
Substitute equation (1) into equation (2) for s:
g + 4g = 25
If [URL='https://www.mathcelebrity.com/1unk.php?num=g%2B4g%3D25&pl=Solve']we plug this equation into our search engine[/URL] and solve for g, we get:
g = [B]5[/B]
Now substitute this into equation 1 for g = 5:
s = 4(5)
s = [B]20[/B]
[B]So George has 5 apples and Sarah has 20 apples[/B]

Georgie joins a gym. she pays $25 to sign up and then $15 each month. Create an equation using this

Georgie joins a gym. she pays $25 to sign up and then $15 each month. Create an equation using this information.
Let m be the number of months Georgie uses the gym. Our equation G(m) is the cost Georgie pays for m months.
G(m) = Variable Cost * m (months) + Fixed Cost
Plug in our numbers:
[B]G(m) = 15m + 25[/B]

Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2

Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2 equations.
Let g be the number of German states. Let a be the number of Austrian states. We're given two equations:
[LIST=1]
[*]a + g = 25
[*]g = a + 7
[/LIST]
To solve this system of equations, we substitute equation (2) into equation (1) for g:
a + (a + 7) = 25
Combine like terms:
2a + 7 = 25
To solve for a, we[URL='https://www.mathcelebrity.com/1unk.php?num=2a%2B7%3D25&pl=Solve'] type this equation into our search engine[/URL] and we get:
[B]a = 9[/B]
To solve for g, we plug in a = 9 into equation (2):
g = 9 + 7
[B]g = 16[/B]

Gino has 7 whole pineapples. He cuts each whole into 4 equal parts. Write an improper fraction for t

Gino has 7 whole pineapples. He cuts each whole into 4 equal parts. Write an improper fraction for the cut parts of pineapples.
Take our whole pineapples divided by the number of equal parts:
[B]7/4[/B]

Giovanni is thinking of a number. If he adds 2 to it, then divides that sum by 3, he gets 7. What is

Giovanni is thinking of a number. If he adds 2 to it, then divides that sum by 3, he gets 7. What is the number?
Let the number be n:
[LIST]
[*]n
[*]Add 2: n + 2
[*]Divide the sum by 3: (n + 2)/3
[*]The word "gets" means an equation, so we set (n + 2)/3 equal to 7
[/LIST]
(n + 2)/3 = 7
Cross multiply:
n + 2 = 21
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B2%3D21&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]19[/B]

Given f = cd^3, f = 450, and d = 10, what is c?

Given f = cd^3, f = 450, and d = 10, what is c?
A) 0.5
B) 4.5
C) 15
D) 45
E) 150
Plugging in our numbers, we get:
c(10)^3 = 450
Since 10^3 = 1000, we have:
1000c = 450
[URL='https://www.mathcelebrity.com/1unk.php?num=1000c%3D450&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]c = 0.45 Answer B[/B]

Given the function f(x)=3x?9, what is the value of x when f(x)=9

Given the function f(x)=3x?9, what is the value of x when f(x)=9
Plug in our numbers and we get:
3x - 9 = 9
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-9%3D9&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]6[/B]

Goal is to take at least 10,000 steps per day. According to your pedometer you have walked 5,274 ste

Goal is to take at least 10,000 steps per day. According to your pedometer you have walked 5,274 steps. Write and solve an inequality to find the possible numbers of steps you can take to reach your goal.
[U]
Subtract off the existing steps (s) from your goal of 10,000[/U]
g >= 10000 - 5274
[B]g >= 4726[/B]
[I]Note: we use >= since 10,000 steps meets the goal as well as anytihng above it[/I]

Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking a

Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. How many minutes will it take until they're at the same altitude?
Set up the Altitude function A(m) where m is the number of minutes that went by since now.
Set up Graham's altitude function A(m):
A(m) = 14040 - 50m <-- we subtract for descending
Set up Max's altitude function A(m):
A(m) = 12500 + 20m <-- we add for ascending
Set the altitudes equal to each other to solve for m:
14040 - 50m = 12500 + 20m
[URL='https://www.mathcelebrity.com/1unk.php?num=14040-50m%3D12500%2B20m&pl=Solve']We type this equation into our search engine to solve for m[/URL] and we get:
m = [B]22[/B]

Grand Mean

Calculates the grand mean of a set of number sets.

Grayson took a total of 16 quizzes over the course of 8 weeks. How many weeks of school will Grayson

Grayson took a total of 16 quizzes over the course of 8 weeks. How many weeks of school will Grayson have to attend this quarter before he will have taken a total of 20 quizzes? Assume the relationship is directly proportional.
Set up a proportion of quizzes to weeks, where w is the number of weeks for 20 quizzes:
16/8 = 20/w
[URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=20&den1=8&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
w = [B]10[/B]

Greatest Common Factor and Least Common Multiple

Given 2 or 3 numbers, the calculator determines the following:

* Greatest Common Factor (GCF) using Factor Pairs

* Rewrite Sum using the Distributive Property and factoring out the GCF

* Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs

* GCF using the method of Successive Division

* GCF using the Prime Factorization method

* Determine if the numbers are coprime and twin prime

* Greatest Common Factor (GCF) using Factor Pairs

* Rewrite Sum using the Distributive Property and factoring out the GCF

* Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs

* GCF using the method of Successive Division

* GCF using the Prime Factorization method

* Determine if the numbers are coprime and twin prime

Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (Think

Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (Think of the monthly charges paid at the end of the month.) Enter the number of months it will take for the total cost for both gyms to be equal.
Gym A cost function C(m) where m is the number of months:
C(m) = Monthly charge * months + Joining Fee
C(m) = 35m + 75
Gym B cost function C(m) where m is the number of months:
C(m) = Monthly charge * months + Joining Fee
C(m) = 60m
Set them equal to each other:
35m + 75 = 60m
To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=35m%2B75%3D60m&pl=Solve']we type this equation into our search engine[/URL] and get:
m = [B]3[/B]

half the sum of the numbers s, t, and u

half the sum of the numbers s, t, and u
The [I]sum [/I]of s, t, and u means we add all 3:
s + t + u
[I]Half[/I] the sum means we divide the sum by 2:
[B](s + t + u)/2[/B]

Hall looked at 10 websites every 35 hours. At this rate, how long, in hours, will it take to look at

Hall looked at 10 websites every 35 hours. At this rate, how long, in hours, will it take to look at 6 websites?
Set up a proportion of websites to hours where h is the number of hours it takes to look at 6 websites:
10/35 = 6/h
To solve this proportion for h, we [URL='https://www.mathcelebrity.com/prop.php?num1=10&num2=6&den1=35&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
h = [B]21 hours[/B]

Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $1

Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $2.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours.
Happy Paws Cost: C = 16 + 1.5h
Woof Watchers: C = 11 + 2.75h
Setup the equation where there costs are equal
16 + 1.5h = 11 + 2.75h
Subtract 11 from each side:
5 + 1.5h = 2.75h
Subtract 1.5h from each side
1.25h = 5
Divide each side by 1.25
[B]h = 4[/B]

Happy Paws charges $19.00 plus $5.50 per hour to keep a dog during the day. Woof Watchers charges $1

Happy Paws charges $19.00 plus $5.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $6.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours.
[B]Happy Paws cost equation:[/B]
5.50h + 19
[B]Woof Watchers cost equation:[/B]
6.75h + 11
[B]Set them equal to each other:[/B]
5.50h + 19 = 6.75h + 11
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=5.50h%2B19%3D6.75h%2B11&pl=Solve']equation solver[/URL], we get [B]h = 6.4[/B].

Hari planted 324 plants in such a way that there were as many rows of plants as there were number of

Hari planted 324 plants in such a way that there were as many rows of plants as there were number of columns. Find the number of rows and columns.
Let r be the number of rows and c be the number of columns. We have the area:
rc = 324
Since rows equal columns, we have a square, and we can set r = c.
c^2 = 324
Take the square root of each side:
[B]c = 18[/B]
Which means [B]r = 18[/B] as well.
What we have is a garden of 18 x 18.

harley had $500 in his bank account at the beginning of the year. he spends $20 each week on food, c

harley had $500 in his bank account at the beginning of the year. he spends $20 each week on food, clothing, and movie tickets. he wants to have more than $100 at the end of summer to make sure he has enough to purchase some new shoes before school starts. how many weeks, w, can harley withdraw money from his savings account and still have more than $100 to buy new shoes?
Let the number of weeks be w. Harley needs $100 (or more) for shoes. We have the balance in Harley's account as:
500 - 20w >= 100
To solve this inequality for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=500-20w%3E%3D100&pl=Solve']type it in our search engine[/URL] and we get:
[B]w <= 20[/B]

He charges $1.50 per delivery and then $2 per km he has to drive to get from his kitchen to the deli

He charges $1.50 per delivery and then $2 per km he has to drive to get from his kitchen to the delivery address. Write an equation that can be used to calculate the delivery price and the distance between the kitchen and the delivery address. Use your equation to calculate the total cost to deliver to someone 2.4km away
Let k be the number of kilometers between the kitchen and delivery address. Our Delivery equation D(k) is:
[B]D(k) = 2k + 1.50[/B]
The problem wants to know D(2.4):
D(2.4) = 2(2.4) + 1.50
D(2.4) = 4.8 + 1.50
D(2.4) = [B]$6.30[/B]

Help

Suppose company A charges a rate of $40 per day and Company B charges a $60 fee plus $40 per day. For what number of days is the cost the same?

Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took

Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took four tests. She scored 10 points better on the second test than she did on the first, 20 points better on the third test than on the first, and 30 points better on the fourth test than on the first. If the mean of these four tests was 70, what was her score on the third test?
Givens:
[LIST]
[*]Let the first test score be s:
[*]The second test score is: s + 10
[*]The third test score is: s + 20
[*]The fourth test score is: s + 30
[/LIST]
The mean of the four tests is 70, found below:
Sum of test scores / Number of Tests = Mean
Plugging in our number, we get:
(s + s + 10 + s + 20 + s + 30) / 4 = 70
Cross multiply and simplify:
4s + 60 = 70 * 4
4s + 60 = 280
To [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B60%3D280&pl=Solve']solve this equation for s, we type it in our search engine[/URL] and we get:
s = 55
So the third test score:
s + 20 = 55 + 20
[B]75[/B]

Heptagonal Number

This calculator determines the nth heptagonal number

Hero cards come in packs of 6. Max has 8 packs of hero cards. He decides to give as many of his frie

Hero cards come in packs of 6. Max has 8 packs of hero cards. He decides to give as many of his friends as he can 9 cards each. How many cards are left over after he does this?
Calculate the number of cards Max starts with:
8 packs * 6 cards per pack = 48 total cards
If he gives as many friends as he can 9 cards each, we want to know how many left over after giving as many friends as he can 9 cards. So we have:
[URL='https://www.mathcelebrity.com/modulus.php?num=48mod9&pl=Calculate+Modulus']48 mod 9[/URL] = [B]3 left over[/B]

Hexagonal Number

This calculator determines the nth hexagonal number

HomeWork Help Please Respond ASAP!!!

[CENTER][B]The Sum of three times a number and 18 is -39. Find the number.[/B][/CENTER]
I was always confused with these problems and never understood them. Any help would be much appreciated!!
Thank you!

HomeWork Help Please Respond ASAP!!!

The phrase a number means an arbitrary variable, let's call it x.
Three times a number:
3x
And 18 means we add 18
3x + 18
The word is means equal to, so we set 3x + 18 equal to -39
3x + 18 = -39
This is your algebraic expression. If you want to solve for x, plug it into the [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']search engine[/URL] and you get x = -19

Hope it's okay to ask this here?

A candy vendor analyzes his sales records and ?nds that if he sells x candy bars in one day, his pro?t(in dollars) is given byP(x) = ? 0.001x2 + 3x ? 1800
(a.) Explain the signi?cance of the number 1800 to the vendor.
(b.) What is the maximum pro?t he can make in one day, and how many candy bars must he sell to
achieve it?
I got 1800 as the amount he starts with, and can't go over. maximum pro?t as 4950
and if I got that right I am getting stuck on how to find how many candy bars.
Thanks

How can you rewrite the number 1 as 2 to a power?

How can you rewrite the number 1 as 2 to a power?
There exists an identity which says, n^0 = 1 where n is a number.
So [B]2^0 = 1[/B]

How many 8$, tickets can I get for 100$

How many 8$, tickets can I get for 100$
Tickets = Total Money / price per ticket
Tickets = 100/8
Tickets = [B]12.5
[/B]
If the problem asks for a whole number, this means you cannot have a partial ticket. Therefore, we round down to [B]12 tickets[/B]

How many nickels are in 3 quarters and 2 dimes

How many nickels are in 3 quarters and 2 dimes
[URL='https://www.mathcelebrity.com/coinvalue.php?p=&n=&d=2&q=3&h=&dol=&pl=Calculate+Coin+Value']3 quarters and 2 dimes[/URL] = 0.95
Since a nickel is 0.05, we have:
Number of nickels = 0.95/0.05
Number of nickels = [B]19[/B]

How many palindromes are between 700 and 800?

How many palindromes are between 700 and 800?
Numeric palindromes are numbers which read the same backwards and forwards. In this case, the number has to start and end with 7.
[LIST=1]
[*]707
[*]717
[*]727
[*]737
[*]747
[*]757
[*]767
[*]777
[*]787
[*]797
[/LIST]
There are [B]10[/B] palindromes between 700 and 800

How many rides per day to reach 150 rides in 90 days?

How many rides per day to reach 150 rides in 90 days?
Set up a proportion of rides per day where r is the number or rides per day:
150/90 = r/1
Type [URL='https://www.mathcelebrity.com/prop.php?num1=150&num2=r&den1=90&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']this proportion into our search engine[/URL] and we get:
r = 1.66 7

How many twelfths equal three-sixths?

How many twelfths equal three-sixths?
We set up the equation below where x is the number of twelfths in three-sixths:
1/12x = 3/6
Cross multiply, and we get:
12x * 3 = 6 * 1
36x = 6
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=36x%3D6&pl=Solve']type this in our math engine[/URL] and we get:
x = [B]1/6 or 0.16667[/B]

How MUCH Change would be returned from a $50.00 bill for the purchase of 26 stainless Steel 8-in. bo

How MUCH Change would be returned from a $50.00 bill for the purchase of 26 stainless Steel 8-in. bolts at the Price Of 79.5 cents each?
Calculate the Stainless Steel Bolts Cost:
Stainless Steel Bolts Cost = Number of Stainless Steel Bolts * Price per bolt
Stainless Steel Bolts Cost = 26 * 0.795
Stainless Steel Bolts Cost = $20.67
Calculate the change:
Change = Cash Offered - Stainless Steel Bolts Cost
Change = $50 - $20.67
Change = [B]$29.33[/B]

I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5

I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5 and add 283. What is my number?
Let the number be n. We're given two expressions:
[LIST=1]
[*]Multiply it by 14 and add 13: 14n + 13
[*]Multiply by 5 and add 283: 5n + 283
[/LIST]
The phrase [I]I get the same answer[/I] means an equation. So we set expression 1 equal to expression 2:
14n + 13 = 5n + 283
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B13%3D5n%2B283&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]30[/B]

I am thinking of a number. I multiply it by 14 and add 21. I get the same answer if I multiply by 4

I am thinking of a number. I multiply it by 14 and add 21. I get the same answer if I multiply by 4 and add 141.
Let the number be n.
We have two expressions:
[LIST=1]
[*]Multiply by 14 and add 21 is written as: 14n + 21
[*]Multiply by 4 and add 141 is written as: 4n + 141
[/LIST]
The phrase [I]get the same expression[/I] means they are equal. So we set (1) and (2) equal to each other and solve for n:
14n + 21 = 4n + 141
[URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B21%3D4n%2B141&pl=Solve']Type this equation into our search engine [/URL]to solve for n and we get:
n = [B]12[/B]

I am Thinking of a number. I multiply it by 3 and add 67. I get the same answer If i multiply by 6 s

I am Thinking of a number. I multiply it by 3 and add 67. I get the same answer If i multiply by 6 subtract 8.
Let the number be n. We're given two equal expressions:
[LIST=1]
[*]3n + 67
[*]6n - 8
[/LIST]
Set the expressions equal to each other since they give the [B]same answer[/B]:
3n + 67 = 6n - 8
We have an equation. [URL='https://www.mathcelebrity.com/1unk.php?num=3n%2B67%3D6n-8&pl=Solve']Type this equation into our search engine and we get[/URL]:
n = [B]25[/B]

I am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 a

I am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 and add 93. What is my number?
Let the number be n. We're given two expressions:
[LIST]
[*]Multiply the number by 7: 7n
[*]add 25: 7n + 25. <-- Expression 1
[*]Multiply by 3: 3n
[*]Add 93: 3n + 93 <-- Expression 2
[*]The phrase [I]get the same answer[/I] means both expression 1 and expression 2 are equal. So we set them equal to each other:
[/LIST]
7n + 25 = 3n + 93
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=7n%2B25%3D3n%2B93&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]17[/B]

I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13

I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13 and subtract 13.What is my number?
Take a number (n):
The first operation is multiply 5 times n, and then add 39:
5n + 139
The second operation is multiply 13 times n and subtract 13:
13n - 13
Set both operations equal to each other since they result in [I]the same number[/I]
5n + 139 = 13n - 13
[URL='https://www.mathcelebrity.com/1unk.php?num=5n%2B139%3D13n-13&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]n = 19[/B]

I have $36 dollars and it goes up by 3 every day how much money would I have after 500 days

I have $36 dollars and it goes up by 3 every day how much money would I have after 500 days
We have a balance function B(d) where d is the number of days passed since we first had $36:
B(d) = 3d + 36
The problem asks for B(500):
B(500) = 3(500) + 36
B(500) = 1500 + 36
B(500) = [B]1536[/B]

I have 150 bags of candy. I need 5 candies for every one bag. How many candies do I need?

I have 150 bags of candy. I need 5 candies for every one bag. How many candies do I need?
Candies = Number of bags * candies per bag
Candies = 150 * 5
Candies = [B]750[/B]

i have 25 pencil cases there are p pencils in each pencil case. how many pencils do i have altogethe

i have 25 pencil cases there are p pencils in each pencil case. how many pencils do i have altogether?
Total pencils = Number of cases * pencils per case
Total pencils = [B]25p[/B]

I make 750 toys in 10 hours how many can I make in 4 minutes

I make 750 toys in 10 hours how many can I make in 4 minutes
Convert 10 hours to 4 minutes so we can compare minutes to minutes:
10 hours * 60 hours per minute = 600 minutes
Now set up a proportion of toys to minutes where t is the number of toys made in 4 minutes:
750/600 = t/4
[URL='https://www.mathcelebrity.com/prop.php?num1=750&num2=t&den1=600&den2=4&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine and we get[/URL]:
t = [B]5[/B]

I only own blue blankets and red blankets. 8 out of every 15 blankets I have are red.

I only own blue blankets and red blankets. 8 out of every 15 blankets I have are red. If have i 45 blankets, how many are blue?
If 8 out of 15 blankets are red, then 15 - 8 = 7 are blue
So 7 out of every 15 blankets are blue.
Set up a proportion of blue blankets to total blankets where b is the number of blue blankets in 45 blankets
7/15 = b/45
Cross multiply:
If 2 proportions are equal, then we can do the following:
Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2
15b = 45 * 7
15b = 315
To solve for b, divide each side of the equation by 15:
15b/15 = 315/15
Cancel the 15's on the left side and we get:
b = [B]21[/B]

I sold 3 units in 563 attempts. How many did I sell per 100 attempts?

I sold 3 units in 563 attempts. How many did I sell per 100 attempts?
Set up a proportion of sales to attempts where s is the number of sales for 100 attempts:
3/563 = s/100
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=s&den1=563&den2=100&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this in our search engine[/URL], we get:
s = [B]0.532 sales[/B]

I think of a number. I multiply it by 6 and add 3. If my answer is 75, calculate the number I starte

I think of a number. I multiply it by 6 and add 3. If my answer is 75, calculate the number I started with.
Let the number be n.
Multiply it by 6:
6n
Add 3:
6n + 3
If the answer is 75, we set 6n + 3 equal to 75:
6n + 3 = 75
We have an equation. To solve for n, [URL='https://www.mathcelebrity.com/1unk.php?num=6n%2B3%3D75&pl=Solve']we type this equation into our search engine[/URL] and get:
[B]n = 12[/B]

If 1/2 cup of milk makes 8 donuts. How much cups it takes to make 28 donuts

If 1/2 cup of milk makes 8 donuts. How much cups it takes to make 28 donuts?
Set up a proportion of cups to donuts, where c is the number of cups required to make 28 donuts:
1/2/8 = c/28
Cross multiply:
28(1/2) = 8c
8c = 14
[URL='https://www.mathcelebrity.com/1unk.php?num=8c%3D14&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]c = 1.75[/B]

If 11 times a number is added to twice the number, the result is 104

If 11 times a number is added to twice the number, the result is 104
Let [I]the number[/I] be an arbitrary variable we call x.
11 times a number:
11x
Twice the number (means we multiply x by 2):
2x
The phrase [I]is added to[/I] means we add 2x to 11x:
11x + 2x
Simplify by grouping like terms:
(11 + 2)x = 13x
The phrase [I]the result is[/I] means an equation, so we set 13x equal to 104:
13x = 104 <-- This is our algebraic expression
To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=13x%3D104&pl=Solve']we type it in our search engine[/URL] and we get:
x = [B]8[/B]

If 115% of a number is 460, what is 75% of the number

If 115% of a number is 460, what is 75% of the number.
Let the number be n. We're given:
115% * n = 460
We write 115% of n as 1.15n, so we have:
1.15n = 460
[URL='https://www.mathcelebrity.com/1unk.php?num=1.15n%3D460&pl=Solve']Using our equation calculator[/URL], we get:
n = [B]400
[/B]
The problem asks for 75% of this number, so we [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=75&den1=400&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type in [I]75% of 400[/I] into our search engine[/URL] and get:
[B]300[/B]

If 12 times a number is added to twice the number, the result is 112

If 12 times a number is added to twice the number, the result is 112.
Let the number be n, so we have:
12n + 2n = 112
Combine like terms
14n = 112
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=14n%3D112&pl=Solve']equation solver[/URL], we get [B]n = 8[/B].

If 2 inches is about 5 centimeters, how many inches are in 25 centimeters? Choose the proportions th

If 2 inches is about 5 centimeters, how many inches are in 25 centimeters? Choose the proportions that accurately represent this scenario.
We set up a proportion of inches to centimeters where i is the number of inches in 25 centimeters:
2/5 = i/25
To solve this proportion for i, we [URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=i&den1=5&den2=25&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
i = [B]10[/B]

If 2 ounces goes into 100 gallons how many ounces is needed for 3000 gallons

If 2 ounces goes into 100 gallons how many ounces is needed for 3000 gallons?
Set up a proportion of ounces to gallons. We set o as the number of ounces for 3000 gallons.
2/100 = o/3000
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=2&num2=o&den1=100&den2=3000&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]o = 60[/B].

If 200 bacteria triple every 1/2 hour, how much bacteria in 3 hours

If 200 bacteria triple every 1/2 hour, how much bacteria in 3 hours
Set up the exponential function B(t) where t is the number of tripling times:
B(d) = 200 * (3^t)
3 hours = 6 (1/2 hour) periods, so we have 6 tripling times. We want to know B(6):
B(6) = 200 * (3^6)
B(6) = 200 * 729
B(6) = [B]145,800[/B]

if 200 is divided in the ratio of 1:3:4 , what is the greatest number

if 200 is divided in the ratio of 1:3:4 , what is the greatest number
Determine the ratio denominator by adding up the ratio amounts:
1 + 3 + 4 = 8
So we have the following ratios and ratio amounts with our greatest number in bold:
[LIST]
[*]1/8 * 200 = 25
[*]3/8 * 200 = 75
[*]4/8 * 200 = [B]100[/B]
[/LIST]

If 25% of a number b is 25.18. What is 20% of b?

If 25% of a number b is 25.18. What is 20% of b?
Using our 25% as 0.25, we have:
0.25b = 25.18
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=0.25x%20%3D%2025.18&pl=Solve']equation calculator[/URL], we get:
b = 100.72
The question asks what is [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=20&den1=100.72&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']20% of 100.72[/URL]. Using our calculator, we get:
[B]20.144[/B]

If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3

If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3
Take this in pieces, where "a number" means an arbitrary variable, let's call it "x".
[LIST=1]
[*]3 times a number --> 3x
[*]3 times a number added to 2 --> 3x + 2
[*]The number plus 4 --> x + 4
[*]is divided by --> (3x + 2)/(x + 4)
[*]the result is 4/3 --> (3x + 2)/(x + 4) = 4/3
[/LIST]

If 3.75 inches on a map are equal to 18.75 miles, how many miles are 5 inches equal to?

If 3.75 inches on a map are equal to 18.75 miles, how many miles are 5 inches equal to?
Set up a proportion of inches to miles where m is the number of miles for 5 inches:
3.75/18.75 = 5/m
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3.75&num2=5&den1=18.75&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
m = [B]25 miles[/B]

If 4 times a number is added to 9, the result is 49

If 4 times a number is added to 9, the result is 49.
[I]A number[/I] means an arbitrary variable, let's call it x.
4 [I]times a number[/I] means we multiply x by 4
4x
[I]Added to[/I] 9 means we add 9 to 4x
4x + 9
[I]The result is[/I] means we have an equation, so we set 4x + 9 equal to 49
[B]4x + 9 = 49[/B] <-- This is our algebraic expression
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D49&pl=Solve']we type it in the search engine[/URL] and get x = 10

If 44% of a number is 120, find 11% of that number.

If 44% of a number is 120, find 11% of that number.
[URL='https://www.mathcelebrity.com/algexpress.php?num=44%ofanumberis120&pl=Write+Expression']44% of a number is 120[/URL]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.44x%20%3D%20120&pl=Solve']Solving for x, we get 272.72[/URL]
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=11&den1=272.727272&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']11% of this is [/URL][B]30[/B]

If 50 out of 250 people die. How many people died per 10 people

If 50 out of 250 people die. How many people died per 10 people
We set up a proportion of deaths to total people where d is the number of deaths for 10 people. We have:
50/250 = d/10
To solve this proportion for d, we [URL='https://www.mathcelebrity.com/prop.php?num1=50&num2=d&den1=250&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
d = [B]2[/B]

If 72 is added to a number it will be 4 times as large as it was originally

If 72 is added to a number it will be 4 times as large as it was originally
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
72 added to a number:
x + 72
4 times as large as it was originally means we take the original number x and multiply it by 4:
4x
Now, the phrase [I]it will be[/I] means an equation, so we set x + 72 equal to 4x to get our final algebraic expression:
[B]x + 72 = 4x[/B]
[B][/B]
If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B72%3D4x&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]24[/B]

If 9 is added to 1/3 of a number, the result is 15. What is the number?

If 9 is added to 1/3 of a number, the result is 15. What is the number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
1/3 of a number means we multiply x by 1/3:
x/3
9 is added to 1/3 of a number:
x/3 + 9
The phrase [I]the result is[/I] means an equation. so we set x/3 + 9 equal to 15
x/3 + 9 = 15
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2F3%2B9%3D15&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]18[/B]

if 9 times a number is decreased by 6, the result is 111

if 9 times a number is decreased by 6, the result is 111
A number means an arbitrary variable, let's call it x.
9 times a number:
9x
Decreased by 6
9x - 6
The result is 11, this means we set 9x - 6 equal to 11
[B]9x - 6 = 11
[/B]
To solve this equation for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=9x-6%3D11&pl=Solve']equation calculator[/URL]

If a die is rolled, what is the probability that the number rolled will not be a "5"?

If a die is rolled, what is the probability that the number rolled will not be a "5"?
Possible rolls:
{1, 2, 3, 4, 5, 6}
Probability of not a 5 means:
{1, 2, 3, 4, 6}
P(Not 6) = 1 - P(6)
P(Not 6) = 1 - 1/6
P(Not 6) = [B]5/6[/B]

if a number is added to its square, it equals 20

if a number is added to its square, it equals 20.
Let the number be an arbitrary variable, let's call it n.
The square of the number means we raise n to the power of 2:
n^2
We add n^2 to n:
n^2 + n
It equals 20 so we set n^2 + n equal to 20
n^2 + n = 20
This is a quadratic equation. So [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn%3D20&pl=Solve+Quadratic+Equation&hintnum=+0']we type this equation into our search engine[/URL] to solve for n and we get two solutions:
[B]n = (-5, 4)[/B]

if a number is added to its square, the result is 72. find the number

if a number is added to its square, the result is 72. find the number.
Let the number be n. We're given:
n + n^2 = 72
Subtract 72 from each side, we get:
n^2 + n - 72 = 0
This is a quadratic equation. [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-72%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']We type this equation into our search engine[/URL], and we get:
[B]n = 8 and n = -9[/B]

if a number is decreased by 5, and then the result is multiplied by 2, the result is 26

If a number is decreased by 5, and then the result is multiplied by 2, the result is 26
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
[I]Decreased by[/I] means we subtract 5 from x:
x - 5
Multiply the result by 2:
2(x - 5)
The result is 26 means we set 2(x - 5) equal to 26:
[B]2(x - 5) = 26[/B]

If a number is increased by 16 and then divided by 3, the result is 8

If a number is increased by 16 and then divided by 3, the result is 8.
Let x be the number. We have:
(x + 16)/3 = 8
Cross multiply
x + 16 = 24
Using our equation calculator, we get:
[B]x = 8[/B]

if a number is tripled the result is 60

if a number is tripled the result is 60
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Triple the number means we multiply by 3:
3x
The phrase [I]the result is[/I] means an equation, so we set 3x equal to 60:
[B]3x = 60 <-- This is our algebraic expression
[/B]
If you want to solve this equation, then [URL='https://www.mathcelebrity.com/1unk.php?num=3x%3D60&pl=Solve']you type in 3x = 60 into the search engine[/URL] and get:
x = 20

If a tutor charges $35 an hour and works for 286 minutes, what is the dollar amount she is owed?

If a tutor charges $35 an hour and works for 286 minutes, what is the dollar amount she is owed?
Dollar Amount Owed = Hourly Rate * Number of Hours Worked
Convert Minutes worked to hours worked
Hours worked = Minutes Worked / 60
Hours worked = 286 minutes / 60 minutes per hour
Hours worked = 4.77
So now back to our main formula...
Dollar Amount Owed = Hourly Rate * Number of Hours Worked
Dollar Amount Owed = $35 * 4.77
Dollar Amount Owed = [B]$166.95[/B]

If an employee starts saving with $750 and increases his savings by 8% each month, what will be his

If an employee starts saving with $750 and increases his savings by 8% each month, what will be his total savings after 10 months?
Set up the savings function S(m), where m is the number of months and I is the interest rate growth:
S(m) = Initial Amount * (1 + i)^m
Plugging in our number at m = 10 months we get:
S(10) = 750 * (1 + 0.08)^10
S(10) = 750 * 1.08^10
S(10) = [B]$1,619.19[/B]

If an experiment is conducted with 5 conditions and 6 subjects in each condition, what are dfn and d

If an experiment is conducted with 5 conditions and 6 subjects in each condition, what are dfn and dfe?
a = Number of groups/conditions = 5
dfn = a - 1
don = 5 - 1
[B]dfn = 4[/B]
N = 5 * 6 = 30
dfe = N - a
dfe = 30 - 5
[B]dfe = 25[/B]

If ben recently paid a $3.77 fine for a book that was 13 days late, what is the daily fine?

If ben recently paid a $3.77 fine for a book that was 13 days late, what is the daily fine?
Daily Fine = Total Fine / Number of Days
Daily Fine = $3.77 / 13 days
Daily Fine = [B]$0.29[/B]

If Bill's salary is $25 and he gets a 20˘ commission on every newspaper he sells, how many must he s

If Bill's salary is $25 and he gets a 20˘ commission on every newspaper he sells, how many must he sell to make $47
Set up bills Earnings function E(n) where n is the number of newspapers he sells:
E(n) =. Cost per newspaper * number of newspapers sold + base salary
E(n) = 0.2n + 25
We're asked to find n when E(n) = 47, so we set E(n) = 47 and solve for n:
0.2n + 25 = 47
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=0.2n%2B25%3D47&pl=Solve']equation solver[/URL], we get:
n = [B]110[/B]

If Emma reads 1 page of a book in 44 seconds, how many pages will she read in 15 minutes

If Emma reads 1 page of a book in 44 seconds, how many pages will she read in 15 minutes
Convert 15 minutes to seconds:
15 minutes = 60 * 15 = 900 seconds
Set up a proportion of pages read to seconds where p is the number of pages read in 900 seconds (15 minutes):
1/44 = p/900
[URL='https://www.mathcelebrity.com/prop.php?num1=1&num2=p&den1=44&den2=900&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
p = [B]20.45[/B]

If half the number is added to twice the number, the answer is 50

If half the number is added to twice the number, the answer is 50.
Let the number be n. Half is also written as 0.5, and twice is written by multiplying by 2. We have:
0.5n + 2n = 50
[URL='https://www.mathcelebrity.com/1unk.php?num=0.5n%2B2n%3D50&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]n = 20[/B]

If I add 8 to the number and then multiply the result by 6 I get the same answer as when I add 58 to

If I add 8 to the number and then multiply the result by 6 I get the same answer as when I add 58 to a number. Form an equation
Let the number be n. We're given:
6(n + 8) = n + 58
Multiply through:
6n + 48 = n + 58
To solve this equation for n, [URL='https://www.mathcelebrity.com/1unk.php?num=6n%2B48%3Dn%2B58&pl=Solve']we type it into our search engine[/URL] and we get:
n = [B]2[/B]

If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it take

If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it take me to read 58 pgs?
Set up a proportion, of reading time to pages where m is the number of minutes it takes you to read 58 pages.
2 hours and 30 minutes is:
60(2) + 30
120 + 30
150 minutes
Our proportion is:
150/93.25 = m/58
[URL='https://www.mathcelebrity.com/prop.php?num1=150&num2=m&den1=93.25&den2=58&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get:
[B]m = 93.3 minutes, or about 1 hour, 33 minutes[/B]

If I make 40,000 dollars every 15 minutes then how long will it take me to make a million

If I make 40,000 dollars every 15 minutes then how long will it take me to make a million
Let f be the number of fifteen minute blocks. We're given:
40000f = 1000000
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=40000f%3D1000000&pl=Solve']type this equation into our search engine[/URL] and we get:
f = 25
Total minutes = Fifteen minute blocks (f) * 15 minutes
Total minutes = 25 * 15
Total minutes = [B]375 minutes or 6 hours and 15 minutes[/B]

If i triple the number then subtract 7 the answer is 2. What is the number

If i triple the number then subtract 7 the answer is 2. What is the number
Let the number be x.
Triple the number:
3x
Subtract 7
3x - 7
The answer is 2 means we set:
[B]3x - 7 = 2[/B]
This is our algebraic expression. To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D2&pl=Solve']we type this problem into the search engine[/URL] and get [B]x = 3[/B].

If n(A)=1200, n(B)=1250 and n(AintersectionB)=320, then n(AUB) is

If n(A)=1200, n(B)=1250 and n(AintersectionB)=320, then n(AUB) is
We know that:
n(AUB) = n(A) + n(B) - n(AintersectionB)
Plugging in our given numbers, we get:
n(AUB) = 1200 + 1250 - 320
n(AUB) = [B]2130[/B]

If one calculator costs d dollars, what is the cost, in dollars, of 13 calculators?

If one calculator costs d dollars, what is the cost, in dollars, of 13 calculators?
Set up cost function C(n), where n is the number of calculators:
C(n) = dn
C(13) = [B]13d[/B]

If one half of a number is 24, what is twice the number?

If one half of a number is 24, what is twice the number?
Let the number be n. We have:
n/2 = 24
Cross multiply, we get n = 48
The problem asks for 2n.
2(48) = [B]96[/B]

if p=2x is even, then p^2 is also even

if p=2x is even, then p^2 is also even
p^2 = 2 * 2 * x^2
p^2 = 4x^2
This is [B]true [/B]because:
[LIST]
[*]If x is even, then x^2 is even since two evens multiplied by each other is even and 4x^2 is even
[*]If x is odd, the x^2 is odd, but 4 times the odd number is always even since even times odd is even
[/LIST]

If the difference of a number and 4 is multiplied by 3 the result is 19

If the difference of a number and 4 is multiplied by 3 the result is 19
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The difference of a number and 4:
x - 4
The phrase [I]is multiplied by[/I] means we multiply x - 4 by 3:
3(x - 4)
The phrase [I]the result is[/I] means equals, so we set 3(x - 4) equal to 19
[B]3(x - 4) = 19
[MEDIA=youtube]Q8bnVJuWeVk[/MEDIA][/B]

If the number of professors in a college is P and the number is students S, and there are 14 times a

If the number of professors in a college is P and the number is students S, and there are 14 times as many students as professors
14 times as many means we multiply:
[B]S = 14P[/B]

If the third of 6 consecutive numbers is 12, what is their sum?

If the third of 6 consecutive numbers is 12, what is their sum?
If 12 is the third of 6 consecutive numbers:
First consecutive number is 12 - 2 = 10
Second consecutive number = 12 - 1 = 11
Third consecutive number = 12
Fourth consecutive number = 12 + 1 = 13
Fifth consecutive number = 13 + 1 = 14
Sixth consecutive number = 14 + 1 = 15
The sum of all consecutive numbers is:
10 + 11 + 12 + 13 + 14 + 15 =[B] 75[/B]

If there are 9000 seconds in 2.5 hours, how many hours are there in 13,500 seconds?

If there are 9000 seconds in 2.5 hours, how many hours are there in 13,500 seconds?
Setup a proportion of hours to seconds where h is the number of hours in 13,500 seconds
2.5/9000 = h/13500
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=2.5&num2=h&den1=9000&den2=13500&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] we get:
h = [B]3.75 hours[/B]

If thrice a number is increased by 11,the result is 35. What is the number

If thrice a number is increased by 11,the result is 35. What is the number?
[LIST]
[*]The phrase [I]a number [/I]means an arbitrary variable. Let's call it x.
[*]Thrice means multiply by 3, so we have 3x
[*]Increased by 11 means we add 11, so we have 3x + 11
[*]The [I]result is[/I] means an equation, so we set 3x + 11 equal to 35
[/LIST]
3x + 11 = 35 <-- This is our algebraic expression
The problem ask us to solve the algebraic expression.
[URL='https://www.mathcelebrity.com/1unk.php?num=3x%2B11%3D35&pl=Solve']Typing this problem into our search engine[/URL], we get [B]x = 8[/B].

If twice a number is divided by 7, the result is -28

If twice a number is divided by 7, the result is -28.
The phrase [I]a number[/I] means an arbitrary variable, let's call it "x".
Twice x means we multiply x by 2: 2x
Divide this by 7: 2x/7
We set this equal to -28, and we have our algebraic expression:
[B]2x/7 = -28 [/B]

If two consecutive even numbers are added, the sum is equal to 226. What is the smaller of the two n

If two consecutive even numbers are added, the sum is equal to 226. What is the smaller of the two numbers?
Let the smaller number be n.
The next consecutive even number is n + 2.
Add them together to equal 226:
n + n + 2 = 226
Solve for [I]n[/I] in the equation n + n + 2 = 226
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(1 + 1)n = 2n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
2n + 2 = + 226
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 2 and 226. To do that, we subtract 2 from both sides
2n + 2 - 2 = 226 - 2
[SIZE=5][B]Step 4: Cancel 2 on the left side:[/B][/SIZE]
2n = 224
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2n/2 = 224/2
n = [B]112
[URL='https://www.mathcelebrity.com/1unk.php?num=n%2Bn%2B2%3D226&pl=Solve']Source[/URL][/B]

if x2 is added to x, the sum is 42

If x2 is added to x, the sum is 42.
x^2 + x = 42
Subtract 42 from both sides:
x^2 + x - 42 = 0
We have a quadratic equation. Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-42%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation solver[/URL], we get:
[B]x = 6 and x = -7
[/B]
Since the problem does not state positive number solutions, they are both answers.

if you add 35 to twice a number, the result is 17. What is the number?

if you add 35 to twice a number, the result is 17. What is the number?
A number is represented by a variable, let's call it "x".
Twice a number means we multiply by 2 --> 2x
Add 35
2x + 35
Now set that entire expression equal to 17
2x + 35 = 17
[URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B35%3D17&pl=Solve']Plug that into the search engine to solve for x[/URL]
[B]x = -9[/B]

If you can buy 1?3 of a box of chocolates for 6 dollars, how much can you purchase for 4 dollars? Wr

If you can buy 1?3 of a box of chocolates for 6 dollars, how much can you purchase for 4 dollars? Write your answer as a fraction of a box.
Set up a proportion of dollars to boxes where b is the number of boxes for $4:
6/1/3 = 4/b
Cross multiply:
6b = 4/3
Multiply each side by 1/6 to isolate b:
b = 4/18
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=4&num2=18&num3=&pl=GCF+and+LCM']Type in GCF(4,18) into the search engine[/URL]. We get a greatest common factor of 2.
Divide 4 and 18 in the fraction by 2. We get the reduced fraction of:
[B]b = 2/9[/B]

If you have $272, and you spend $17 each day, how long would it be until you had no money left?

If you have $272, and you spend $17 each day, how long would it be until you had no money left?
Let d be the number of days. We have a balance expression of:
272 - 17d
We want to know when the balance is 0, so we set 272 - 17d equal to 0.
272 - 17d = 0
To solve for d, we [URL='http://272 - 17d = 0']type this equation into our search engine[/URL] and we get:
d = [B]16[/B]

If you triple a number and then add 10, you get one-half of the original number. What is the number

If you triple a number and then add 10, you get one-half of the original number. What is the number?
Let the number be n. We have:
3n + 10 = 0.5n
Subtract 0.5n from each side
2.5n + 10 = 0
Subtract 10 from each side:
2.5n = -10
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2.5n%3D-10&pl=Solve']equation calculator,[/URL] we get:
[B]n = -4[/B]

If you triple me, subract 7, and add 4 you get 42. What number am i?

If you triple me, subract 7, and add 4 you get 42. What number am i?
Start with an unknown number, "x".
Triple me
3x
Subtract 7
3x - 7
Add 4
3x - 7 + 4
You get 42
3x - 7 + 4 = 42
Simplify:
3x - 3 = 42
Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=3x-3%3D42&pl=Solve']equation calculator:[/URL]
x = [B]15[/B]

If your parents give you $20 per week and $1.50 per chore, how many chores would you have to do to e

If your parents give you $20 per week and $1.50 per chore, how many chores would you have to do to earn a total of $33.50 that week?
Let c be the number of chores. We're given the equation:
1.50c + 20 = 33.50
To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.50c%2B20%3D33.50&pl=Solve']type it in our search engine [/URL]and we get:
c = [B]9[/B]

Imaginary Numbers

Calculates the imaginary number i where i = √-1 raised to any integer power as well as the product of imaginary numbers of quotient of imaginary numbers

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What's the sample [U][B]standard deviation[/B][/U]?
[B]20.79182532[/B] using stdev.s in excel or also found on our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics#standard_deviation']statistics calculator[/URL]

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What's the [B][U]standard error of the mean[/U][/B]?
9.29839 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics#standard_error_of_the_mean']statistics calculator[/URL]

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. The researcher posed a null hypothesis that the average weight for boys in that high school should be 100 lbs. What is the [B][U]absolute value[/U][/B] of calculated t that we use for testing the null hypothesis?
Mean is 109.4 and Standard Deviation = 20.79182532 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']statistics calculator[/URL]
Now use those values and calculate the t-value
Abs(t value) = (100 - 109.4)/ 20.79182532/sqrt(5)
Abs(tvalue) = [B]1.010928029[/B]

In 2010 a algebra book cost $125. In 2015 the book cost $205. Whats the linear function since 2010?

In 2010 a algebra book cost $125. In 2015 the book cost $205. Whats the linear function since 2010?
In 5 years, the book appreciated 205 - 125 = 80 in value.
80/5 = 16.
So each year, the book increases 16 in value. Set up the cost function:
[B]C(y) = 16y where y is the number of years since 2010[/B]

In 2010, the population of Greenbow, AL was 1,100 people. The population has risen at at rate of 4%

In 2010, the population of Greenbow, AL was 1,100 people. The population has risen at at rate of 4% each year since. Let x = the number of years since 2010 and y = the population of Greenbow. What will the population of Greenbow be in 2022?
P(x) = 1,100(1.04)^x
x = 2022 - 2010
x = 12 years
We want P(12):
P(12) = 1,100(1.04)^12
P(12) = 1,100(1.60103221857)
P(12) = [B]1,761.14 ~ 1,761[/B]

In a basketball game, you make 8 of 20 free throws. If you continue this for the next 50 free throws

In a basketball game, you make 8 of 20 free throws. If you continue this for the next 50 free throws, how many can you expect to make?
We set up a [U][I]proportion[/I][/U] of made free throws to attempts.
8/20 = m/50 where m is the number of made free throws in 50 attempts.
[URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=m&den1=20&den2=50&propsign=%3D&pl=Calculate+missing+proportion+value']We type 8/20 = m/50 into the search engine[/URL] and get [B]m = 20[/B].

In a bike shop they sell bicycles & tricycles. I counted 80 wheels & 34 seats. How many bicycles & t

In a bike shop they sell bicycles & tricycles. I counted 80 wheels & 34 seats. How many bicycles & tricycles were in the bike shop?
Let b be the number or bicycles and t be the number of tricycles. Since each bicycle has 2 wheels and 1 seat and each tricycle has 3 wheels and 1 seat, we have the following equations:
[LIST=1]
[*]2b + 3t = 80
[*]b + t = 34
[/LIST]
We can solve this set of simultaneous equations 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2b+%2B+3t+%3D+80&term2=b+%2B+t+%3D+34&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2b+%2B+3t+%3D+80&term2=b+%2B+t+%3D+34&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2b+%2B+3t+%3D+80&term2=b+%2B+t+%3D+34&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]b = 22[/B]
[*][B]t = 12[/B]
[/LIST]

In a car lot there are 38 rows with 25 parking spots in each row. How many parking spots are there?

In a car lot there are 38 rows with 25 parking spots in each row. How many parking spots are there?
Total parking spots = Number of Rows * Parking spots per row
Total parking spots = 38 * 25
Total parking spots = [B]950[/B]

In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there i

In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there in the class?
We start by declaring variables for boys and girls:
[LIST]
[*]Let b be the number of boys
[*]Let g be the number of girls
[/LIST]
We're given two equations:
[LIST=1]
[*]b = g + 5
[*]b + g = 13
[/LIST]
Substitute equation (1) for b into equation (2):
g + 5 + g = 13
Grouping like terms, we get:
2g + 5 = 13
Subtract 5 from each side:
2g + 5 - 5 = 13 - 5
Cancel the 5's on the left side and we get:
2g = 8
Divide each side of the equation by 2 to isolate g:
2g/2 = 8/2
Cancel the 2's on the left side and we get:
g = 4
Substitute g = 4 into equation (1) to solve for b:
b = 4 + 5
b = [B]9[/B]

In a newspaper, it was reported that yearly robberies in Springfield were up 40% to 77 in 2012 from

In a newspaper, it was reported that yearly robberies in Springfield were up 40% to 77 in 2012 from 2011. How many robberies were there in Springfield in 2011?
Let r be the number of robberies in 2011. We have:
Robberies in 2012 = Robberies in 2011 * 1.4
77 = r * 1.4
Divide each side by 1.4
[B]r = 55[/B]

In a sample of 80 beetles, 50 beetles had 4 spots each, and the rest had 6 spots each. What was the

In a sample of 80 beetles, 50 beetles had 4 spots each, and the rest had 6 spots each. What was the average number of spots per beetle? Show your work below.
Average spots per beetle = Total spots for all beetles / Total beetles
Average spots per beetle = (50(4) + 6(80 - 50))/80
Average spots per beetle =(200 + 6(30))/80
Average spots per beetle = (200 + 180)/80
Average spots per beetle = (380)/80
Average spots per beetle = [B]4.75 spots[/B]

In a shipment of 330 animals, 125 were hogs, 68 were sheep, and the rest were cattle. Find the numbe

In a shipment of 330 animals, 125 were hogs, 68 were sheep, and the rest were cattle. Find the number of cattle in the shipment.
To find the rest (cattle), we subtract off the hogs and sheep from the total.
Cattle = Total Animals - Hogs - Sheep
Cattle = 330 - 125 - 68
[B]Cattle = 137[/B]

In a survey of 420 people, 230 use samsung mobile, 180 use iphone, 90 use both ,find the number of p

In a survey of 420 people, 230 use samsung mobile, 180 use iphone, 90 use both ,find the number of people who don't use either of them
People who don't use both is:
420 - (230 + 180 - 90)
420 - (320)
[B]100[/B]

In base 10 the number 25.12 actually means 20 + 5 + 1/10 + 2/100. What does the base 7 number 25.12

In base 10 the number 25.12 actually means 20 + 5 + 1/10 + 2/100. What does the base 7 number 25.12 mean?
2 groups of 7
5 groups of 1
1 group of 1/7
2 groups of 1/49 (1/7)^2
14 + 5 + 1/7 + 2/49

In base 10, the number .1111... approaches 1/9. What does .111111 base 2 approach in base 10?

In base 10, the number .1111... approaches 1/9. What does .111111 base 2 approach in base 10?
Base 2 .11111 means:
(1/2)^1 + (1/2)^2 + + (1/2)^3 + (1/2)^4
1/2 + 1/4 + 1/8 + 1/16
[B]This approaches 1[/B]

In one day, a store sells 14 pairs of jeans. The 14 jeans represent 20% of the total number of items

In one day, a store sells 14 pairs of jeans. The 14 jeans represent 20% of the total number of items sold that day. How many items did the store sell in one day? Explain or show how you got your answer.
14 = 20%s where s is the number of items sold in one day.
We can write 20% as 0.2, so we have:
0.2s = 14
[URL='https://www.mathcelebrity.com/1unk.php?num=0.2s%3D14&pl=Solve']Type this equation into the search engine[/URL], and we get:
s = [B]70[/B]

In rolling a die, the event E is getting a number greater than or equal to 3. What is the complement

In rolling a die, the event E is getting a number greater than or equal to 3. What is the complement of the event?
The complement E' is everything but the event. So we have:
E = P(n >= 3)
E' = [B]P(n < 3)[/B]

In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing

In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game? In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game?
Let w be the winning team's points, and l be the losing team's points. We have two equations:
[LIST=1]
[*]w + l = 41
[*]w - l = 27
[/LIST]
Add the two equations:
2w = 68
Divide each side by 2
[B]w = 34[/B]
Substitute this into (1)
34 + l = 41
Subtract 34 from each side
[B]l = 7[/B]
Check your work:
[LIST=1]
[*]34 + 7 = 41 <-- check
[*]34 - 7 = 27 <-- check
[/LIST]
The final score of the game was [B]34 to 7[/B].
You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=w+%2B+l+%3D+41&term2=w+-+l+%3D+27&pl=Cramers+Method']simultaneous equation solver[/URL].

In the wild, monkeys eat an average of 28 bananas a day with a standard deviation of 2 bananas. One

In the wild, monkeys eat an average of 28 bananas a day with a standard deviation of 2 bananas. One monkey eats only 21 bananas. What is the z-score for this monkey? Is the number of bananas the monkey eats unusually low?
Using [URL='https://www.mathcelebrity.com/probnormdist.php?xone=21&mean=28&stdev=2&n=1&pl=P%28X+%3C+Z%29']our z-score calculator[/URL], we get:
Z < -3.5
P(Z < -3.5) = 0.499767
Also, this [B]is unusually low as it's more than 3 deviations away from the mean[/B]

In the year 2000, the population of Rahway, New Jersey, was 26500. Express this number in scientific

In the year 2000, the population of Rahway, New Jersey, was 26500. Express this number in scientific notation
26,500 in [URL='https://www.mathcelebrity.com/scinot.php?num=26500&pl=Convert+to+Number']scientific notation is found using our scientific notation calculator[/URL]:
[B]2.65 x 10^4[/B]

In this class of 4/5 students are right handed. if there are 20 right handed students, what is the t

In this class of 4/5 students are right handed. if there are 20 right handed students, what is the total number of students in this class?
Let x be the total number of students in the class. We have:
4/5x = 20
Cross multiplying or using our [URL='http://www.mathcelebrity.com/1unk.php?num=4x%3D100&pl=Solve']equation calculator[/URL], we get:
4x = 100
Divide each side by 4
[B]x = 25[/B]

Ina has $40 in her bank account and saves $8 a week. Ree has $200 in her bank account and spends $12

Ina has $40 in her bank account and saves $8 a week. Ree has $200 in her bank account and spends $12 a week. Write an equation to represent each girl.
Let w equal the number of weeks, and f(w) be the amount of money in the account after w weeks:
[LIST]
[*]Ina: [B]f(w) = 40 + 8w[/B]
[LIST]
[*]We add because Ina saves money, so her account grows
[/LIST]
[*]Ree: [B]f(w) = 200 - 12w[/B]
[LIST]
[*]We subtract because Ree saves
[/LIST]
[/LIST]

Inclusive Number Word Problems

Given an integer A and an integer B, this calculates the following inclusive word problem questions:

1) The Average of all numbers inclusive from A to B

2) The Count of all numbers inclusive from A to B

3) The Sum of all numbers inclusive from A to B

1) The Average of all numbers inclusive from A to B

2) The Count of all numbers inclusive from A to B

3) The Sum of all numbers inclusive from A to B

Index Form

Writes a number using index form notation

index form of (5^3)^6

Index form of (5^3)^6
Index form is written as a number raised to a power.
Let's simplify by multiply the exponents. Since 6*3 = 18, We have:
[B]5^18[/B]

Int Function

Determines the integer of a number

Irrational Numbers Between

This calculator determines all irrational numbers between two numbers

Is (3,10) a solution to the equation y=4x

Is (3,10) a solution to the equation y=4x
Plug in the numbers to check:
10 ? 4(3)
10 <> 12
No, this is [B]not a solution[/B]

Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how many hours sh

Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how many hours she needs to work to earn at least $120.
A few things to note:
[LIST]
[*]Earnings = Rate * time
[*]Let h be the number of hours worked
[*]The phrase [I]at least[/I] means greater than or equal to, so we have the following inequality.
[/LIST]
We represent this with the following inequality:
7.5h < 120
To solve this inequality for h, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=7.5h%3C120&pl=Show+Interval+Notation']type it into our math engine[/URL] and we get:
[B]h < 16[/B]

Isabel is making face mask. She spends $50 on supplies and plans on selling them for $4 per mask. Ho

Isabel is making face mask. She spends $50 on supplies and plans on selling them for $4 per mask. How many mask does have to make in order to make a profit equal to $90?
[U]Set up the cost function C(m) where m is the number of masks:[/U]
C(m) = supply cost
C(m) = 50
[U]Set up the cost function R(m) where m is the number of masks:[/U]
R(m) = Sale Price * m
R(m) = 4m
[U]Set up the profit function P(m) where m is the number of masks:[/U]
P(m) = R(m) - C(m)
P(m) = 4m - 50
The problems asks for profit of 90, so we set P(m) = 90:
4m - 50 = 90
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=4m-50%3D90&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]35[/B]

Isabel will run less than 36 minutes today. So far, she has run 22 minutes. What are the possible nu

Isabel will run less than 36 minutes today. So far, she has run 22 minutes. What are the possible numbers of additional minutes she will run?
Set up our inequality. If she ran 22 minutes, we need to find an expression to find out the remaining minutes
x + 22 < 36
Subtract 22 from each side:
x < 14
Remember, she cannot run negative minutes, so our lower bound is 0, so we have:
[B]0 < x < 14
[/B]

Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only

[SIZE=4]Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only 5 times as old as William?
[U]Express Ishaan and William's age since today where y is the number of years since today, we have:[/U]
i = 72+y
w = 4+y
[U]We want the time for Ishaan age will be 5 times William's age:[/U]
i = 5w
72 + y = 5(4 + y)
We [URL='https://www.mathcelebrity.com/1unk.php?num=72%2By%3D5%284%2By%29&pl=Solve']plug this equation into our search engine [/URL]and get:
y = [B]13[/B]
[/SIZE]

It costs $2.50 to rent bowling shoes. Each game costs $2.25. You have $9.25. How many games can you

It costs $2.50 to rent bowling shoes. Each game costs $2.25. You have $9.25. How many games can you bowl. Writing an equation and give your answer.
Let the number of games be g. we have the function C(g):
C(g) = cost per game * g + bowling shoe rental
C(g) = 2.25g + 2.50
The problem asks for g when C(g) = 9.25
2.25g + 2.50 = 9.25
To solve this equation, we[URL='https://www.mathcelebrity.com/1unk.php?num=2.25g%2B2.50%3D9.25&pl=Solve'] type it in our search engine[/URL] and we get:
g = [B]3[/B]

it costs $75.00 for a service call from shearin heating and air conditioning company. the charge for

it costs $75.00 for a service call from shearin heating and air conditioning company. the charge for labor is $60.00 . how many full hours can they work on my air conditioning unit and still stay within my budget of $300.00 for repairs and service?
Our Cost Function is C(h), where h is the number of labor hours. We have:
C(h) = Variable Cost * Hours + Fixed Cost
C(h) = 60h + 75
Set C(h) = $300
60h + 75 = 300
[URL='https://www.mathcelebrity.com/1unk.php?num=60h%2B75%3D300&pl=Solve']Running this problem in the search engine[/URL], we get [B]h = 3.75[/B].

It costs a $20 flat fee to rent a lawn mower, plus $5 a day starting with the first day. Let x repre

It costs a $20 flat fee to rent a lawn mower, plus $5 a day starting with the first day. Let x represent the number of days rented, so y represents the charge to the user (in dollars)
Set up our function:
[B]y = 20 + 5x[/B]

It is known that 45% of men snore an 25% of women snore. A doctor looked at these numbers and made t

It is known that 45% of men snore an 25% of women snore. A doctor looked at these numbers and made the following statement:
"If you put a man and a woman together, there is a 70% chance that someone is snoring."
Explain why the doctor's math is wrong.
The doctor added the percents together: 45% + 25% = 70%.
Here's why this is incorrect:
[LIST]
[*]45% of men snore means 100% - 45% = 55% of men do not snore
[*]25% of women snore means 100% - 25% = 75% of women do not snore
[*]Both men and women not snoring is: 55% * 75% = 41.25% neither of them snore
[*]100% - 41.25% = [B]58.75%[/B] somebody is snoring
[/LIST]

It takes 3/4 of an hour to complete a puzzle. How many puzzles can Cindy finish in 3 hours?

It takes 3/4 of an hour to complete a puzzle. How many puzzles can Cindy finish in 3 hours?
We setup a proportion of time to puzzles where p is the number of puzzles Cindy can complete in 3 hours:
3/4/1 = 3/p
Dividing by 1 means the same as the original fraction, so we have:
3/4 = 3/p
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=3&den1=4&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into the search engine[/URL], we get:
p = [B]4[/B]

It took 3.5 gallons of paint to cover a wall that is 985 square feet. How many gallons will it take

It took 3.5 gallons of paint to cover a wall that is 985 square feet. How many gallons will it take to cover a wall that is 6501 square feet?
Set up a proportion of gallons of paint to square feet where n is the number of gallons of paint to cover 6501 square feet
3.5/985 = n/6501
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3.5&num2=n&den1=985&den2=6501&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
n = [B]23.1[/B]

Itachi want’s to buy apples that weights 5.7 pounds. The apples is priced at $1.58 per pound how muc

Itachi want’s to buy apples that weights 5.7 pounds. The apples is priced at $1.58 per pound how much does the apples costs
Cost = price per pound * number of pounds
Cost = 1.58 * 5.7
Cost = [B]9.01[/B]

Jack and Jill have a magic pail of beans. The number of beans in the pail doubles every second. If

Jack and Jill have a magic pail of beans. The number of beans in the pail doubles every second. If the pail is full after 10 seconds, when was the pail half full? Explain your answer.
[LIST]
[*]At time 0, we have n beans
[*]At time 1, we have 2n beans
[*]At time 2, we have 4n beans
[*]At time 3, we have 8n beans
[*]At time 4, we have 16n beans
[*]At time 5, we have 32n beans
[*]At time 6, we have 64n beans
[*]At time 7, we have 128n beans
[*]At time 8, we have 256n beans
[*]At time 9, we have 512n beans
[*]At time 10, we have 1024n beans
[/LIST]
1/2 of 1024 is 512, so at [B]Time 9[/B], the pail is half full.

Jack bought 7 tickets for a movie. He paid $7 for each adult ticket and $4 for each child ticket. Ja

Jack bought 7 tickets for a movie. He paid $7 for each adult ticket and $4 for each child ticket. Jack spent $40 for the tickets
Let a = Number of adult tickets and c be the number of child tickets.
[LIST=1]
[*]7a + 4c = 40
[*]a + c = 7
[*]Rearrange (2): a = 7 - c
[/LIST]
Now substitute a in (3) into (1):
7(7 - c) + 4c = 40
49 - 7c + 4c = 40
49 - 3c = 40
Add 3c to each side and subtract 40:
3c = 9
Divide each side by 3:
[B]c = 3
[/B]
Substitute c = 3 into Equation (2)
a + 3 = 7
Subtract 3 from each side:
[B]a = 4[/B]

Jack bought a car for $17,500. The car loses $750 in value each year. Which equation represents the

Jack bought a car for $17,500. The car loses $750 in value each year. Which equation represents the situation?
Let y be the number of years since Jack bought the car. We have a Book value B(y):
[B]B(y) = 17500 - 750y[/B]

Jack has 34 bills and coins in 5’s and 2’s. The total value is $116. How many 5 dollar bills does he

Jack has 34 bills and coins in 5’s and 2’s. The total value is $116. How many 5 dollar bills does he have?
Let the number of 5 dollar bills be f. Let the number of 2 dollar bills be t. We're given two equations:
[LIST=1]
[*]f + t = 34
[*]5f + 2t = 116
[/LIST]
We have a system of equations, which we can solve 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answers:
[LIST]
[*][B]f = 16[/B]
[*][B]t = 18[/B]
[/LIST]

Jack is making snack bags. He has 18 baby carrots and 42 pretzels. He wants to divide them equally a

Jack is making snack bags. He has 18 baby carrots and 42 pretzels. He wants to divide them equally among the bags. What is the greatest number of snack bags he can make?
Find the [URL='http://www.mathcelebrity.com/gcflcm.php?num1=18&num2=42&num3=&pl=GCF']Greatest Common Factor[/URL] of (18, 42) = 6
6 bags for 18 carrots = 3 carrots per bag
6 bags for 42 pretzels = 7 pretzels per bag
[B]6 bags is the answer[/B]

Jack reads 90 pages of a book in six hours. What is the average number of pages he read each hour

Jack reads 90 pages of a book in six hours. What is the average number of pages he read each hour
90 pages / 6 hour = 90/6
Type [URL='https://www.mathcelebrity.com/fraction.php?frac1=90%2F6&frac2=3%2F8&pl=Simplify']90/6 in our search engine, click simplify[/URL], and we get:
[B]15 pages per hour[/B]

Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocola

Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
If Jack had 2 chocolates left, then the total given to his friends is:
50 - 2 = 48
Let f be the number of friends at his birthday party. Then we have:
3f = 48
[URL='https://www.mathcelebrity.com/1unk.php?num=3f%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]f = 16[/B]

Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocola

Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
Let f be the number of Jacks's friends. We have the following equation to represent the chocolates:
3f + 2 = 50
To solve this equation for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=3f%2B2%3D50&pl=Solve']type it in the math engine[/URL] and we get:
f = [B]16[/B]

Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episod

Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episode airs, Jake receives a bunch of fan mail. He splits all the letters into 3 equal stacks to open with his mom and his sister. Each stack contains 21 letters. Which equation can you use to find the number of letters n Jake receives?
The number of letters n is represented by number of stacks (s) times letter per stack (l). We're given s = 3 and l = 21, so we have:
n = 21(3)
n = [B]63[/B]

James has a weekly allowance of 5 plus 1.50 for each chore c he does

James has a weekly allowance of 5 plus 1.50 for each chore c he does
We build the allowance function A(c) where c is each chore
A(c) = cost per chore * c + Weekly Allowance
Plugging in our numbers, we get:
[B]A(c) = 1.50c + 5[/B]

Jamie spent $15.36 on several items at the store. he spent an equal amount on each item. if jamie sp

Jamie spent $15.36 on several items at the store. he spent an equal amount on each item. if jamie spent $1.92 on each item, how many items did he buy?
Let x equal the number of items Jamie bought. We have:
1.92x = 15.36
Divide each side by 1.92
[B]x = 8[/B]

Jane did this calculation a. Add -12 b.subtract -9 c. Add 8 d. Subtract -2 the result is -5. What wa

Jane did this calculation a. Add -12 b.subtract -9 c. Add 8 d. Subtract -2 the result is -5. What was the original number?
Let the original number be n.
[LIST=1]
[*]Add -12: n - 12
[*]Subtract -9: n - 12 - -9 = n - 12 + 9
[*]Add 8: n - 12 + 9 + 8
[*]Subtract - 2: n - 12 + 9 + 8 - -2 = n - 12 + 9 + 8 + 2
[*]The result is -5. So we build the following equation:
[/LIST]
n - 12 + 9 + 8 + 2 = -5
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n-12%2B9%2B8%2B2%3D-5&pl=Solve']type it in our search engine[/URL] and we get:
[B]n = -12[/B]

Jane has $7.50 to spend in the candy store. She likes lollipops and gumballs. Each lollipop costs

Jane has $7.50 to spend in the candy store. She likes lollipops and gumballs. Each lollipop costs $2.75, and each gumball costs $0.50. If Jane decides to buy 1 lollipop, then what is the greatest number of gumballs Jane can buy? A
Subtract the cost of 1 lollipop:
$7.50 - $2.75 = $4.75
Let the number of gumballs = g. We have:
0.50g = $4.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.50g%3D4.75&pl=Solve']Run this through the search engine[/URL] to get g = 9.5 The problem asks for the greatest number. So we round down to [B]9 gumballs[/B].

jane has 55$ to spend at cedar point. the admission price is 42$ and each soda is 4.25. write an ine

jane has 55$ to spend at cedar point. the admission price is 42$ and each soda is 4.25. write an inequality to show how many sodas he can buy.
Let s be the number of sodas.
Cost for the day is:
Price per soda * s + Admission Price
4.25s + 42
We're told that Jane has 55, which means Jane cannot spend more than 55. Jane can spend up to or less than 55. We write this as an inequality using <= 55
[B]4.25s + 42 <= 55[/B]
[B][/B]
If the problems asks you to solve for s, we type it in our math engine and we get:
Solve for [I]s[/I] in the inequality 4.25s + 42 ? 55
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 42 and 55. To do that, we subtract 42 from both sides
4.25s + 42 - 42 ? 55 - 42
[SIZE=5][B]Step 2: Cancel 42 on the left side:[/B][/SIZE]
4.25s ? 13
[SIZE=5][B]Step 3: Divide each side of the inequality by 4.25[/B][/SIZE]
4.25s/4.25 ? 13/4.25
[B]s ? 3.06[/B]

Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling?

Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling?
Distance = Rate * Time
We're given D = 395 and t = 5
We want Rate. We divide each side of the equation by time:
Distance / Time = Rate * Time / Time
Cancel the Time's on each side and we get:
Rate = Distance / Time
Plugging our numbers in, we get:
Rate = 395/5
Rate = [B]79 kilometers[/B]

Janice is looking to buy a vacation home for $185,000 near her favorite southern beach. The formula

Janice is looking to buy a vacation home for $185,000 near her favorite southern beach. The formula to compute a mortgage payment, M, is shown below, where P is the principal amount of the loan, r is the monthly interest rate, and N is the number of monthly payments. Janice's bank offers a monthly interest rate of 0.325% for a 12-year mortgage. How many monthly payments must Janice make?
12 years * 12 months per year = [B]144 mortgage payments[/B]

jared bakes 2 apple pies. he cuts two pies into pieces. Each piece is 1/8 of a pie. Enter the number

jared bakes 2 apple pies. he cuts two pies into pieces. Each piece is 1/8 of a pie. Enter the number of pieces of pie jared cuts
1/8 of a pie per slice means there are 8 slices per pie
2 pies * 8 pieces per pie = [B]16 pieces[/B]

Jason has an equal number of nickels and dimes. The total value of his nickels and dimes is $2.25. H

Jason has an equal number of nickels and dimes. The total value of his nickels and dimes is $2.25. How many nickels does Jason have?
Let the number of nickels be n
Let the number of dimes be d
We're given two equations:
[LIST=1]
[*]d = n
[*]0.05n + 0.1d = 2.25
[/LIST]
Substitute equation (1) for d into equation (2):
0.05n + 0.1n = 2.25
Solve for [I]n[/I] in the equation 0.05n + 0.1n = 2.25
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(0.05 + 0.1)n = 0.15n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
0.15n = + 2.25
[SIZE=5][B]Step 3: Divide each side of the equation by 0.15[/B][/SIZE]
0.15n/0.15 = 2.25/0.15
n = [B]15[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05n%2B0.1n%3D2.25&pl=Solve']Source[/URL]

Jay has 5 paintings that he plans to display on a wall that only has 4 books. Nancy has 5 paintings

Jay has 5 paintings that he plans to display on a wall that only has 4 books. Nancy has 5 paintings that she plans to display on a wall with 5 hooks. Who has more possible ways to hang his/her paintings?
Jay's ways:
[URL='https://www.mathcelebrity.com/permutation.php?num=5&den=4&pl=Permutations']5 P 4 [/URL]= [B]120
[/B]
Nancy's ways:
[URL='https://www.mathcelebrity.com/permutation.php?num=5&den=5&pl=Permutations']5 P 5[/URL] = [B]120
Therefore, they have the same number of ways.[/B]

Jayden spent $46.20 on 12 galllons of gasoline. What was the price per gallon?

Jayden spent $46.20 on 12 galllons of gasoline. What was the price per gallon?
Price per gallon = Total spend / number of gallons
Price per gallon = $46.20/12
Price per gallon = $[B]3.85[/B]

Jazmin is a hairdresser who rents a station in a salon for daily fee. The amount of money (m) Jazmin

Jazmin is a hairdresser who rents a station in a salon for daily fee. The amount of money (m) Jazmin makes from any number of haircuts (n) a day is described by the linear function m = 45n - 30
A) A haircut costs $30, and the station rent is $45
B) A haircut costs $45, and the station rent is $30.
C) Jazmin must do 30 haircuts to pay the $45 rental fee.
D) Jazmin deducts $30 from each $45 haircut for the station rent.
[B]Answer B, since rent is only due once. Profit is Revenue - Cost[/B]

Jeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An em

Jeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An employee in the Amazon distribution center earns about $13 an hour. The estimated lifespan of the employee is 71 years. If the employee worked 24 hours a day, every day of the year from the moment of his birth, how many lifespans would it take for him to earn wages equivalent to Jeff Bezos' net worth? Round the answer to the nearest whole number.
Calculate earnings per lifespan:
Earnings per lifespan = lifespan in years * Annual Earnings
Earnings per lifespan = 71 * 13 * 24 * 365 <-- (24 hours per day * 365 days per year)
Earnings per lifespan = 8,085,480
Calculate the number of lifespans needed to match Jeff Bezos earnings:
Number of lifespans = Jeff Bezos Net Worth / Earnings Per Lifespan
Number of lifespans = 143,100,000,000 / 8,085,480
Number of lifespans = [B]17,698.39 ~ 17,699[/B]

Jeni sees 104 octopus legs in the aquarium how many octopuses are there ?

Jeni sees 104 octopus legs in the aquarium how many octopuses are there ?
An octopus has 8 legs. So the total number of octupuses are:
Total octopuses = Total legs / 8
Total octopuses = 104 / 8
Total octopuses = [B]13[/B]

Jennifer is playing cards with her bestie when she draws a card from a pack of 25 cards numbered fro

Jennifer is playing cards with her bestie when she draws a card from a pack of 25 cards numbered from 1 to 25. What is the probability of drawing a number that is square?
The squares from 1 - 25 less than or equal to 25 are as follows:
[LIST=1]
[*]1^2 = 1
[*]2^2 = 4
[*]3^2 = 9
[*]4^2 = 16
[*]5^2 = 25
[/LIST]
So the following 5 cards are squares:
{1, 4, 9, 16, 25}
Therefore, our probability of drawing a square is:
P(square) = Number of Squares / Number of Cards
P(square) = 5/25
This fraction can be simplified. So [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F25&frac2=3%2F8&pl=Simplify']we type in 5/25 into our search engine, choose simplify[/URL], and we get:
P(square) = [B]1/5[/B]

Jennifer spent $11.25 on ingredients for cookies shes making for the school bake sale. How many cook

Jennifer spent $11.25 on ingredients for cookies shes making for the school bake sale. How many cookies must she sale at $0.35 apiece to make profit?
Let x be the number of cookies she makes. To break even, she must sell:
0.35x = 11.25
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.35x%3D11.25&pl=Solve']equation calculator[/URL], and we get:
x = 32.14
This means she must sell [B]33[/B] cookies to make a profit.

Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how many

Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how many weeks will Jenny and Kelsey have the same amount of money?
Jenny: Let w be the number of weeks. Spending means we subtract, so we set up a balance equation B(w):
B(w) = 1200 - 40w
Kelsey: Let w be the number of weeks. Saving means we add, so we set up a balance equation B(w):
B(w) = 120 + 50w
When they have the same amount of money, we set the balance equations equal to each other:
1200 - 40w = 120 + 50w
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=1200-40w%3D120%2B50w&pl=Solve']type this equation into our search engine[/URL] and we get:
w = [B]12[/B]

Jenny makes 9 dollars for each hour of work. Write an equation to represent her total pay p after wo

Jenny makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Since Jenny makes 9 dollars for each hour of work, then her total pay (p) is her hourly rate times the number of hours worked:
[B]p = 9h[/B]

Jenny went shoe shopping. Now she has 5 more pairs than her brother. Together they have 25 pairs. Ho

Jenny went shoe shopping. Now she has 5 more pairs than her brother. Together they have 25 pairs. How many pairs does Jenny have and how many pairs does her brother have?
[U]Let j be the number of shoes Jenny has and b be the number of s hoes her brother has. Set up 2 equations:[/U]
(1) b + j = 25
(2) j = b + 5
[U]Substitute (2) into (1)[/U]
b + (b + 5) = 25
[U]Group the b terms[/U]
2b + 5 = 25
[U]Subtract 5 from each side[/U]
2b = 20
[U]Divide each side by b[/U]
[B]b = 10
[/B]
[U]Substitute b = 10 into (2)[/U]
j = 10 + 5
[B]j = 15[/B]

Jeremy can plant 10 trees in 4 hours. How many trees can he plant in 10 hours?

Jeremy can plant 10 trees in 4 hours. How many trees can he plant in 10 hours?
Set up a proportion of trees planted to hours where t is the number of trees planted in 10 hours.
10/4 = t/10
[URL='https://www.mathcelebrity.com/prop.php?num1=10&num2=t&den1=4&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']Type this expression into the search engine[/URL] and we get [B]t = 25[/B].
This means Jeremy can plant 25 trees in 10 hours.

Jerry rolls a dice 300 times what is the estimated numbers the dice rolls on 6

Jerry rolls a dice 300 times what is the estimated numbers the dice rolls on 6
Expected Value = Rolls * Probability
Since a 6 has a probability of 1/6, we have:
Expected Value = 300 * 1/6
Expected Value = [B]50[/B]

Jerry’s Bakery makes 144 muffins daily. How many muffins do they make in 7 days? Explain.

Jerry’s Bakery makes 144 muffins daily. How many muffins do they make in 7 days? Explain.
Total muffins = Muffins per day * number of days
Total muffins = 144 * 7
Total muffins = [B]1,008[/B]

Jessica has 16 pairs of shoes. She buys 2 additional pair of shoes every month. What is the slope in

Jessica has 16 pairs of shoes. She buys 2 additional pair of shoes every month. What is the slope in this situation?
Set up a graph where months is on the x-axis and number of shoes Jessica owns is on the y-axis.
[LIST=1]
[*]Month 1 = (1, 18)
[*]Month 2 = (2, 20)
[*]Month 3 = (3, 22)
[*]Month 4 = (4, 24)
[/LIST]
You can see for every 1 unit move in x, we get a 2 unit move in y.
Pick any of these 2 points, and [URL='https://www.mathcelebrity.com/slope.php?xone=3&yone=22&slope=+2%2F5&xtwo=4&ytwo=24&pl=You+entered+2+points']use our slope calculator[/URL] to get:
Slope = [B]2[/B]

Jill made 122 muffins. She put them into 3 boxes and has two muffins left. How many are in each box

Jill made 122 muffins. She put them into 3 boxes and has two muffins left. How many are in each box if they all contain the same amount of muffins?
Let m equal the number of muffins per box.
We're told that we have 3 boxes and 2 muffins left after filling up all 3 boxes.
3m + 2 = 122
To solve for m, we subtract 2 from each side:
3m + 2 - 2 = 122 - 2
Cancel the 2's on the left side and we get:
3m = 120
Divide each side by 3 to isolate m:
3m/3 = 120/3
Cancel the 3's on the left side and we get:
m = [B]40[/B]

Jim has $440 in his savings account and adds $12 per week to the account. At the same time, Rhonda h

Jim has $440 in his savings account and adds $12 per week to the account. At the same time, Rhonda has $260 in her savings account and adds $18 per week to the account. How long will it take Rhonda to have the same amount in her account as Jim?
[U]Set up Jim's savings function S(w) where w is the number of weeks of savings:[/U]
S(w) = Savings per week * w + Initial Savings
S(w) = 12w + 440
[U]Set up Rhonda's savings function S(w) where w is the number of weeks of savings:[/U]
S(w) = Savings per week * w + Initial Savings
S(w) = 18w + 260
The problems asks for w where both savings functions equal each other:
12w + 440 = 18w + 260
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=12w%2B440%3D18w%2B260&pl=Solve']type this equation into our math engine[/URL] and we get:
w = [B]30[/B]

Jim was thinking of a number. Jim adds 20 to it, then doubles it and gets an answer of 99.2. What wa

Jim was thinking of a number. Jim adds 20 to it, then doubles it and gets an answer of 99.2. What was the original number?
Start with x.
Add 20 to it
x + 20
Double it
2(x + 20)
Set this equal to 99.2
2(x + 20) = 99.2
Divide each side by 2:
x + 20 = 49.6
Subtract 20 from each side:
x = [B]29.6[/B]

Jim works for his dad and earns $400 every week plus $22 for every chair (c) he sells. Write an equa

Jim works for his dad and earns $400 every week plus $22 for every chair (c) he sells. Write an equation that can be used to determine jims weekly salary (S) given the number of chairs (c) he sells.
[B]S(c) = 400 + 22c[/B]

Jina's test score average decreased by 10 points this semester. Write a signed number to represent t

Jina's test score average decreased by 10 points this semester. Write a signed number to represent this change in average.
Let A be the original average. The new average is:
A + (-10)

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 76 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.
At least means greater than or equal to, so we have:
[B]3x + 4y >= 76[/B]

Jody is buying a scrapbook and sheets of designer paper. She has $40 and needs at least $18.25 to bu

Jody is buying a scrapbook and sheets of designer paper. She has $40 and needs at least $18.25 to buy the scrapbook. Each sheet of paper costs $0.34. How many sheets of paper can she buy?
Set up a cost equation for the number of pieces of paper (p):
0.34p + 18.25 <= 40 <-- we have an inequality since we can't go over 40
[URL='https://www.mathcelebrity.com/1unk.php?num=0.34p%2B18.25%3C%3D40&pl=Solve']Type this inequality into our search engine[/URL] and we get:
p <= 63.97
We round down, so we get p = [B]63[/B].

Joe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his sal

Joe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his sales were $100,235. How much money did he earn in May?
[U]The commission and salary formula is:[/U]
Earnings = Salary + Commission Percent * Sales
Plugging in our numbers with 4% as 0.04, we get:
Earnings = 500 + 0.04 * 100235
Earnings = 500 + 4009.40
Earnings = [B]4,509.40[/B]

Joe opens a bank account that starts with $20 and deposits $10 each week. Bria has a different accou

Joe opens a bank account that starts with $20 and deposits $10 each week. Bria has a different account that starts with $1000 but withdraws $15 each week. When will Joe and Bria have the same amount of money?
Let w be the number of weeks. Deposits mean we add money and withdrawals mean we subtract money.
[U]Joe's Balance function B(w) where w is the number of weeks:[/U]
20 + 10w
[U]Bria's Balance function B(w) where w is the number of weeks:[/U]
1000 - 15w
[U]The problem asks for when both balances will be the same. So we set them equal to each other and solve for w:[/U]
20 + 10w = 1000 - 15w
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=20%2B10w%3D1000-15w&pl=Solve']type this equation into our search engine[/URL] and we get:
w = 39.2
We round up to full week and get:
w = [B]40[/B]

joe plans to watch 3 movies each month. white an equation to represent the total number of movies n

joe plans to watch 3 movies each month. white an equation to represent the total number of movies n that he will watch in m months
Build movie equation. 3 movies per month at m months means we multiply:
[B]n = 3m[/B]

Joel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. Which

Joel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. Which system of linear equations represents the given situation?
Let a be the number of the $13 book, and b equal the number of $17 books. We have the following system of linear equations:
[LIST=1]
[*][B]a + b = 88[/B]
[*][B]13a + 17b = 128[/B]
[/LIST]
To solve this system, use our calculator for the following methods:
[LIST]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Substitution']Substitution[/URL]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Elimination']Elimination[/URL]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]

Joelle had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil co

Joelle had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?
Subtract the $10 left over from the $24 Joelle started with.
$24 - $10 = $14
Therefore, Joelle spent $14 on seven pencils.
Cost per pencil = Total Pencil Spend / Number of pencils
Cost per pencil = 14 / 7
Cost per pencil = [B]$2[/B]

Joey and Romnick play in the same soccer team. Last Saturday, Romnick scored 3 more goals than Joey,

Joey and Romnick play in the same soccer team. Last Saturday, Romnick scored 3 more goals than Joey,but together they scored less than 9 goals. What are the possible number of goal Romnick scored?
Let j be Joey's goals
Let r by Romnick's goals
We're given 1 equation and 1 inequality:
[LIST=1]
[*]r = j + 3
[*]r + j < 9
[/LIST]
Rearranging equation 1 for j, we have:
[LIST=1]
[*]j = r - 3
[*]r + j < 9
[/LIST]
Substitute equation (1) into inequality (2) for j:
r + r - 3 < 9
2r - 3 < 9
[URL='https://www.mathcelebrity.com/1unk.php?num=2r-3%3C9&pl=Solve']Typing this inequality into our math engine[/URL], we get:
[B]r < 6[/B]

John has x number of marbles. His friend gave him 6 marbles more. Write an expression for the total

John has x number of marbles. His friend gave him 6 marbles more. Write an expression for the total number of marbles John now has.
More means we add:
[B]x + 6[/B]

John is paid a retainer of $550 a week as well as a 2% commission on sales made. Find his income for

John is paid a retainer of $550 a week as well as a 2% commission on sales made. Find his income for the week if in one week he sells cars worth of $80000
Set up the income function C(s) where s is the number of sales for a week. Since 2% can be written as 0.02, we have:
I(s) = Retainer + 2% of sales
I(s) = 550 + 0.02s
The problem asks for a I(s) where s = 80,000:
I(s) = 550 + 0.02(80000)
I(s) = 550 + 1600
I(s) = [B]2150[/B]

John read the first 114 pages of a novel, which was 3 pages less than 1/3

John read the first 114 pages of a novel, which was 3 pages less than 1/3
Set up the equation for the number of pages (p) in the novel
1/3p - 3 = 114
Add 3 to each side
1/3p = 117
Multiply each side by 3
[B]p = 351[/B]

John read the first 114 pages of a novel, which was 3 pages less than 1/3 of the novel.

John read the first 114 pages of a novel, which was 3 pages less than 1/3 of the novel.
Let n be the number of pages in the novel. We have:
1/3n - 3 = 114
Multiply each side by 3:
n - 9 = 342
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=n-9%3D342&pl=Solve']equation solver[/URL], we get [B]n = 351[/B].

John spent $10.40 on 5 notebooks and 5 pens. Ariana spent $7.00 on 4 notebooks and 2 pens. What is t

John spent $10.40 on 5 notebooks and 5 pens. Ariana spent $7.00 on 4 notebooks and 2 pens. What is the ost of 1 notebook and what is the cost of 1 pen?
Let the number of notebooks be n and the number of pens be p. We have two equations:
[LIST=1]
[*]5n + 5p = 10.40
[*]4n + 2p = 7
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=5n+%2B+5p+%3D+10.40&term2=4n+%2B+2p+%3D+7&pl=Cramers+Method']simultaneous equation calculator[/URL], we have:
[LIST]
[*][B]n = 1.42[/B]
[*][B]p = 0.66[/B]
[/LIST]

Jordan has already scored 153 points this basketball season. If he scores 17 points per game, which

Jordan has already scored 153 points this basketball season. If he scores 17 points per game, which inequality represents the number of addional games he needs to play in order to score at least 255 points for the season?
Let g be the number of games Jordan plays. Total points per game is 17g. And he’s already scored 153. So we need 17g + 153 to be [I]at least [/I]255. The phrase at least means greater than or equal to, so we use the >= operator for our inequality:
[B]17g + 153 >= 255[/B]

Jordan practices his trombone for 45 minutes each day. Write an expression for the number of minutes

Jordan practices his trombone for 45 minutes each day. Write an expression for the number of minutes Jordan practices she practices the trombone in d days.
Let m = the number of minutes practiced. We ave:
[B]m = 45d[/B]

Jose has scored 556 points on his math tests so far this semester. To get an A for the semester, he

Jose has scored 556 points on his math tests so far this semester. To get an A for the semester, he must score at least 660 points. Write and solve an inequality to find the minimum number of points he must score on the remaining tests, n, in order to get an A.
We want to know n, such that 556 + n >= 660. <-- We use >= symbol since at least means greater than or equal to.
556 + n >= 660
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=556%2Bn%3E%3D660&pl=Solve']equation/inequality calculator[/URL], we get [B]n >= 104[/B]

Josh earns $25 per week for cleaning his room. He cleaned his room for 7 weeks. How much money did J

Josh earns $25 per week for cleaning his room. He cleaned his room for 7 weeks. How much money did Josh earn?
Total Earnings = Room cleaning Fee Per Week * Number of Weeks
Total Earnings = $25 * 7
Total Earnings = [B]$175[/B]

Juan has d dimes and q quarters in his pocket. The total value of the coins is less than $14.75. Whi

Juan has d dimes and q quarters in his pocket. The total value of the coins is less than $14.75. Which inequality models this situation?
[U]Let d be the number of dimes and q be the number of quarters[/U]
[B]0.1d + 0.25q < 14.75[/B]

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and .10 cents for additional texts. How many texts did she send out?
Let m be the number of messages. We have a cost function of:
C(m) = 9 + 0.1(m - 600)
We are given C(m) = 18.20
18.20 = 9 + 0.1(m - 600)
18.20 = 9 + 0.1m - 60
Combine like terms:
18.20 = 0.1m - 51
Add 51 to each side
0.1m = 69.20
Divide each side by 0.1
[B]m = 692[/B]

Julie has $300 to plan a dance. There is a one-time fee of $75 to reserve a room. It also costs $1.5

Julie has $300 to plan a dance. There is a one-time fee of $75 to reserve a room. It also costs $1.50 per person for food and drinks. What is the maximum number of people that can come to the dance?
Let each person be p. We have the following relationship for cost:
1.50p + 75 <=300
We use the <= sign since we cannot go over the $300 budget.
[URL='https://www.mathcelebrity.com/1unk.php?num=1.50p%2B75%3C%3D300&pl=Solve']We type this inequality into our search engine[/URL], and we get:
p <= 150
Since we have the equal sign within the inequality, the maximum number of people that can come to the dance is [B]150.[/B]

Julie has $48 to spend at a carnival. The carnival charges $8 for admission and $5 per ride. What is

Julie has $48 to spend at a carnival. The carnival charges $8 for admission and $5 per ride. What is the maximum number of rides Julie can go on?
Subtract admission charges, since that money is gone:
$48 - $8 = $40 left over
If rides cost $5, we can go on $40/$5 = [B]8 rides[/B] maximum.

Julio had a coin box that consisted of only quarters and dimes. The number of quarters was three tim

Julio had a coin box that consisted of only quarters and dimes. The number of quarters was three times the number of dimes. If the number of dimes is n, what is the value of coins in the coin box?
Set up monetary value:
[LIST]
[*]Value of the dimes = 0.1n
[*]Value of the quarters = 0.25 * 3n = 0.75n
[/LIST]
Add them together
[B]0.85n[/B]

Julio has $150. Each week, he saves an additional $10. Write a function f(x) that models the total a

Julio has $150. Each week, he saves an additional $10. Write a function f(x) that models the total amount of money Julio has after x weeks
f(x) = Savings per week * number of weeks + starting amount
f(x) = [B]10x + 150[/B]

Julius Caesar was born and 100 BC and was 66 years old when he died in which year did he die?

Julius Caesar was born and 100 BC and was 66 years old when he died in which year did he die?
BC means "Before Christ". On a timeline, it represents a negative number, where year 0 is the birth of Christ. So we have -100 + 66 = -34
-34 means [B]34 BC[/B].

Kaitlin is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the nu

Kaitlin is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of Math is Fun she sells. Suppose that x and y are related by the equation 2500+110x=y. What is Kaitlin totalm pay if she doesnt sell any copies of Math is Fun?
We want the value of y when x = 0.
y = 2500 + 110(o)
y = 2500 + 0
[B]y = 2500[/B]

Karen bought a bucket of popcorn at the movies for $5. She also bought some candy for $2 each. Karen

Karen bought a bucket of popcorn at the movies for $5. She also bought some candy for $2 each. Karen has to spend less than $15 on the popcorn and candy. Which inequality can be used to find c, the number of candies that Karen could have bought?
Since the candy cost is the product of price and quantity, we have:
2c + 5 < 15
To solve this inequality for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=2c%2B5%3C15&pl=Solve']type it in our math engine [/URL]and we get:
[B]c < 5[/B]

Karen earns $20 per hour and already has $400 saved, and wants to save $1200. How many hours until b

Karen earns $20 per hour and already has $400 saved, and wants to save $1200. How many hours until bob gets his $1200 goal?
Set up he savings function S(h) where h is the number of hours needed:
S(h) = savings per hour * h + current savings amount
S(h) = 20h + 400
The question asks for h when S(h) = 1200:
20h + 400 = 1200
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B400%3D1200&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]40[/B]

Karen wants to buy new shoes. There is a promotion for 3 pairs of sneakers for $450.75, how much wou

Karen wants to buy new shoes. There is a promotion for 3 pairs of sneakers for $450.75, how much would one pair of sneakers cost?
Cost per sneaker = Total Cost / number of sneakers
Cost per sneaker = 450.75/3
Cost per sneaker = [B]150.25[/B]

Karin has 3 to spend in the arcade. The game she likes costs 50c per play. What are the possible num

Karin has 3 to spend in the arcade. The game she likes costs 50c per play. What are the possible numbers of times that she can play?
[U]Let x = the number of games Karin can play with her money[/U]
0.5x = 3
[U]Divide each side by 0.5[/U]
[B]x = 6[/B]

Karmen just got hired to work at Walmart. She spent $15 on her new uniform and she gets paid $8 per

Karmen just got hired to work at Walmart. She spent $15 on her new uniform and she gets paid $8 per hour. Write an equation that represents how much money she profits after working for a certain number of hours. How many hours will she have to work for in order to buy a new snowboard ( which costs $450)
Her profit equation P(h) where h is the number of hours worked is:
[B]P(h) = 8h - 15[/B]
Note: [I]We subtract 15 as the cost of Karmen's uniform.
[/I]
Next, we want to see how many hours Karmen must work to buy a new snowboard which costs $450.
We set the profit equation equal to $450
8h - 15 = 450
[URL='https://www.mathcelebrity.com/1unk.php?num=8h-15%3D450&pl=Solve']Typing 8h - 15 = 450 into the search engine[/URL], we get h = 58.13. We round this up to 59 hours.

Kayla has $1500 in her bank account. She spends $150 each week. Write an equation in slope-intercept

Kayla has $1500 in her bank account. She spends $150 each week. Write an equation in slope-intercept form that represents the relationship between the amount in Kayla's bank account, A, and the number of weeks she has been spending, w
[LIST]
[*]Slope intercept form is written as A = mw + b
[*]m = -150, since spending is a decrease
[*]b = 1500, since this is what Kayla starts with when w = 0
[/LIST]
[B]A = -150w + 1500[/B]

keisha is babysitting at 8$ per hour to earn money for a car. So far she has saved $1300. The car th

keisha is babysitting at 8$ per hour to earn money for a car. So far she has saved $1300. The car that keisha wants to buy costs at least $5440. How many hours does Keisha need to babysit to earn enough to buy the car
Set up the Earning function E(h) where h is the number of hours Keisha needs to babysit:
E(h) = 8h + 1300
The question asks for h when E(h) is at least 5440. The phrase [I]at least[/I] means an inequality, which is greater than or equal to. So we have:
8h + 1300 >= 5440
To solve this inequality, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h%2B1300%3E%3D5440&pl=Solve']type it in our search engine[/URL] and we get:
h >= [B]517.5[/B]

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 a

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account.
Keith's balance is written as B(w) where w is the number of weeks passed since the beginning of summer. We have:
B(w) = 500 - 25w
The problem asks for B(w) = 200, so we set 500 - 25w = 200.
[URL='https://www.mathcelebrity.com/1unk.php?num=500-25w%3D200&pl=Solve']Typing 500 - 25w = 200 into the search engine[/URL], we get [B]w = 12[/B].

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 a

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account
Our account balance is:
500 - 25w where w is the number of weeks.
We want to know the following for w:
500 - 25w = 200
[URL='https://www.mathcelebrity.com/1unk.php?num=500-25w%3D200&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 12[/B]

Keith is going to Renaissance Festival with $120 to pay for his admission, food and the cost of game

Keith is going to Renaissance Festival with $120 to pay for his admission, food and the cost of games. He spends a total of $85 on admission and food. Games cost $5 each. Which inequality models the maximum number of games Keith can play.
Let the number of games be g. Keith can spend less than or equal to 120. So we have
[B]5g + 85 <= 120
[/B]
If we want to solve the inequality for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=5g%2B85%3C%3D120&pl=Solve']type it in our search engine[/URL] and we have:
g <= 7

Kellie has only $5.25 to buy breakfast. She wants to buy as many carrot muffins as she can. Each muf

Kellie has only $5.25 to buy breakfast. She wants to buy as many carrot muffins as she can. Each muffin costs $0.75. What’s an equation?
Let m be the number of muffins. Cost equals price * quantity, so we have:
[B]0.75m = 5.25
[/B]
To solve the equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75m%3D5.25&pl=Solve']type the equation into our search engine[/URL] and we get:
m = [B]7[/B]

Kendra has $5.70 in quarters and nickels. If she has 12 more quarters than nickels, how many of each

Kendra has $5.70 in quarters and nickels. If she has 12 more quarters than nickels, how many of each coin does she have?
Let n be the number of nickels and q be the number of quarters. We have:
[LIST=1]
[*]q = n + 12
[*]0.05n + 0.25q = 5.70
[/LIST]
Substitute (1) into (2)
0.05n + 0.25(n + 12) = 5.70
0.05n + 0.25n + 3 = 5.70
Combine like terms:
0.3n + 3 = 5.70
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.3n%2B3%3D5.70&pl=Solve']equation calculator[/URL], we get [B]n = 9[/B].
Substituting that back into (1), we get:
q = 9 + 12
[B]q = 21[/B]

Kerry asked a bank teller to cash 390 check using 20 bills and 50 bills. If the teller gave her a to

Kerry asked a bank teller to cash 390 check using 20 bills and 50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive?
Let t = number of 20 bills and f = number of 50 bills. We have two equations.
(1) 20t + 50f = 390
(2) t + f = 15
[U]Rearrange (2) into (3) for t, by subtracting f from each side:[/U]
(3) t = 15 - f
[U]Now substitute (3) into (1)[/U]
20(15 - f) + 50f = 390
300 - 20f + 50f = 390
[U]Combine f terms[/U]
300 + 30f = 390
[U]Subtract 300 from each side[/U]
30f = 90
[U]Divide each side by 30[/U]
[B]f = 3[/B]
[U]Substitute f = 3 into (3)[/U]
t = 15 - 3
[B]t = 12[/B]

Kevin and Randy Muise have a jar containing 52 coins, all of which are either quarters or nickels.

Kevin and Randy Muise have a jar containing 52 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $6.20. How many of each type of coin do they have?
Let q be the number of quarters, and n be the number of nickels. We have:
[LIST=1]
[*]n + q = 52
[*]0.05n + 0.25q = 6.20
[/LIST]
We can solve this system of equations three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+q+%3D+52&term2=0.05n+%2B+0.25q+%3D+6.20&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+q+%3D+52&term2=0.05n+%2B+0.25q+%3D+6.20&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+q+%3D+52&term2=0.05n+%2B+0.25q+%3D+6.20&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter what method we choose, we get the same answer:
[LIST]
[*][B]n = 34[/B]
[*][B]q = 18[/B]
[/LIST]

Kierra had $35 to spend at the movies. If it was $11 to get in and snacks were 2$ each, how many sna

Kierra had $35 to spend at the movies. If it was $11 to get in and snacks were 2$ each, how many snacks could she buy?
Subtract off cover charge:
35 - 11 = 24
Let s equal the number of snacks Kierra can buy. With each snack costing $2, we have the following equation:
2s = 24
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2s%3D24&pl=Solve']equation calculator[/URL], we have:
[B]s = 12[/B]

kim and jason just had business cards made. kim’s printing company charged a one time setup fee of $

kim and jason just had business cards made. kim’s printing company charged a one time setup fee of $8 and then $20 per box of cards. jason,meanwhile ordered his online. they cost $8 per box. there was no setup fee, but he had to pay $20 to have his order shipped to his house. by coincidence, kim and jason ended up spending the same amount on their business cards. how many boxes did each buy? how much did each spend?
Set up Kim's cost function C(b) where b is the number of boxes:
C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee
C(b) = 20c + 8 + 0
Set up Jason's cost function C(b) where b is the number of boxes:
C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee
C(b) = 8c + 0 + 20
Since Kim and Jason spent the same amount, set both cost equations equal to each other:
20c + 8 = 8c + 20
[URL='https://www.mathcelebrity.com/1unk.php?num=20c%2B8%3D8c%2B20&pl=Solve']Type this equation into our search engine[/URL] to solve for c, and we get:
c = 1
How much did they spend? We pick either Kim's or Jason's cost equation since they spent the same, and plug in c = 1:
Kim:
C(1) = 20(1) + 8
C(1) = 20 + 8
C(1) = [B]28
[/B]
Jason:
C(1) = 8(1) + 20
C(1) = 8 + 20
C(1) = [B]28[/B]

Kim earns $30 for babysitting on Friday nights. She makes an average of $1.25 in tips per hour. Writ

Kim earns $30 for babysitting on Friday nights. She makes an average of $1.25 in tips per hour. Write the function of Kim's earnings, and solve for how much she would make after 3 hours.
Set up the earnings equation E(h) where h is the number of hours. We have the function:
E(h) = 1.25h + 30
The problem asks for E(3):
E(3) = 1.25(3) + 30
E(3) = 4.75 + 30
E(3) = [B]$34.75[/B]

kim wants to buy candy for 4 dollars a pound. if she wants to spend less than 20 dollars, how many b

kim wants to buy candy for 4 dollars a pound. if she wants to spend less than 20 dollars, how many bags can she buy
Since cost = price * quantity, we have the following inequality with b as the number of bags:
4b < 20
To solve this inequality for b, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4b%3C20&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]b < 5[/B]

Kim, Jenny, and Wendy are basketball players. Each plays a different position (guard, forward, and c

Kim, Jenny, and Wendy are basketball players. Each plays a different position (guard, forward, and center) and wears a different number (30, 32, and 35).Kim and number 30 are too small to play center. Number 35 is the center. Neither Kim nor Wendy is the forward. Who plays guard, and what uniform number does she wear?
[LIST]
[*]Kim does not play center
[*]Kim does not play forward
[*]Which means [B]Kim is the guard[/B]
[*]Since Kim is not number 30, and she cannot be number 35 since Number 35 is the center, the only number left is [B]Number 32[/B]
[/LIST]
[B]Kim is the guard with number 32[/B]

Kimberly takes 4 pages of notes during each hour of class. Write an equation that shows the relation

Kimberly takes 4 pages of notes during each hour of class. Write an equation that shows the relationship between the time in class x and the number of pages y.
With x hours and y pages, our equation is:
[B]y = 4x [/B]

Kimberly wants to become a member of the desert squad at a big catering company very badly, but she

Kimberly wants to become a member of the desert squad at a big catering company very badly, but she must pass three difficult tests to do so. On the first Terrifying Tiramisu test she scored a 68. On the second the challenging Chocalate-Sprinkled Creme Brulee she scored a 72. If kimberly needs an average of 60 on all three tests to become a member on the squad what is the lowest score she can make on her third and final test
This is a missing average problem.
Given 2 scores of 68, 72, what should be score number 3 in order to attain an average score of 60?
[SIZE=5][B]Setup Average Equation:[/B][/SIZE]
Average = (Sum of our 2 numbers + unknown score of [I]x)/[/I]Total Numbers
60 = (68 + 72 + x)/3
[SIZE=5][B]Cross Multiply[/B][/SIZE]
68 + 72 + x = 60 x 3
x + 140 = 180
[SIZE=5][B]Subtract 140 from both sides of the equation to isolate x:[/B][/SIZE]
x + 140 - 140 = 180 - 140
x = [B]40[/B]

Kristen and Julia went skating. Julia skated 30 minutes longer than Kristen. If Julia skated for 55

Kristen and Julia went skating. Julia skated 30 minutes longer than Kristen. If Julia skated for 55 minutes, write and solve an equation to find how long Kristen skated
Let j be the number of minutes Julia skates and k be the number of minutes Kristen skated. We have 2 equations:
[B](1) j = k + 30
(2) j = 55[/B]
[U]Plug (2) into (1)[/U]
j = 55 + 30
[B]j = 85 minutes, or 1 hour and 25 minutes[/B]

Krutika was thinking of a number. Krutika doubles it and adds 8.7 to get an answer of 64.9. Form an

Krutika was thinking of a number. Krutika doubles it and adds 8.7 to get an answer of 64.9. Form an equation with x from the information.
[LIST=1]
[*]The number we start with is x.
[*]Double it means we multiply by 2: 2x
[*]Add 8.7: 2x + 8.7
[*][I]Get an answer[/I] means we have an equation, so we set (3) above equal to 64.9
[*][B]2x + 8.7 = 64.9[/B]
[/LIST]
If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B8.7%3D64.9&pl=Solve']equation calculator[/URL].

Lagrange Four Square Theorem (Bachet Conjecture)

Builds the Lagrange Theorem Notation (Bachet Conjecture) for any natural number using the Sum of four squares.

Lamar had N record albums that he tried to sell at a garage sale for $5 each. If the number of recor

Lamar had N record albums that he tried to sell at a garage sale for $5 each. If the number of record albums he didn't sell is called Q, how much money did Lamar get from record album sales?
Sales = Price * (Albums had - Albums sold)
[B]Sales = 5(N - Q)[/B]

larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2

larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2 numbers
Declare Variables for each number:
[LIST]
[*]Let l be the larger number
[*]Let s be the smaller number
[/LIST]
We're given two equations:
[LIST=1]
[*]l = s + 12
[*]l + s = 74
[/LIST]
Equation (1) already has l solved for. Substitute equation (1) into equation (2) for l:
s + 12 + s = 74
Solve for [I]s[/I] in the equation s + 12 + s = 74
[SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE]
(1 + 1)s = 2s
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
2s + 12 = + 74
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 12 and 74. To do that, we subtract 12 from both sides
2s + 12 - 12 = 74 - 12
[SIZE=5][B]Step 4: Cancel 12 on the left side:[/B][/SIZE]
2s = 62
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2s/2 = 62/2
s = [B]31[/B]
To solve for l, we substitute in s = 31 into equation (1):
l = 31 + 12
l = [B]43[/B]

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?
Declare variables for the 2 numbers:
[LIST]
[*]Let l be the larger number
[*]Let s be the smaller number
[/LIST]
We're given two equations:
[LIST=1]
[*]l = s + 4
[*]l + s = 40
[/LIST]
To get this problem in terms of the larger number l, we rearrange equation (1) in terms of l.
Subtract 4 from each side in equation (1)
l - 4 = s + 4 - 4
Cancel the 4's and we get:
s = l - 4
Our given equations are now:
[LIST=1]
[*]s = l - 4
[*]l + s = 40
[/LIST]
Substitute equation (1) into equation (2) for s:
l + l - 4 = 40
Grouping like terms for l, we get:
2l - 4 = 40
Add 4 to each side:
2l - 4 + 4 = 40 + 4
Cancelling the 4's on the left side, we get
2l = 44
Divide each side of the equation by 2 to isolate l:
2l/2 = 44/2
Cancel the 2's on the left side and we get:
l = [B]22[/B]

Larry is buying new clothes for his return to school. He is buying shoes for $57 and shirts cost $15

Larry is buying new clothes for his return to school. He is buying shoes for $57 and shirts cost $15 each. He has $105 to spend. Which of the following can be solved to find the number of shirts he can afford?
Let s be the number of shirts. Since shoes are a one-time fixed cost, we have:
15s + 57 = 105
We want to solve this equation for s. We [URL='https://www.mathcelebrity.com/1unk.php?num=15s%2B57%3D105&pl=Solve']type it in our math engine[/URL] and we get:
s = [B]3.2 or 3 whole shirts[/B]

Last week at the business where you work, you sold 120 items. The business paid $1 per item and sol

Last week at the business where you work, you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items?
Let n be the number of items. We have the following equations:
Cost Function C(n) = n
For n = 120, we have C(120) = 120
Revenue Function R(n) = 3n
For n = 120, we have R(120) = 3(120) = 360
Profit = Revenue - Cost
Profit = 360 - 120
Profit = [B]240[/B]

last week, bill drove 252 miles. This week, he drove m miles. Using m , write an expression for the

last week, bill drove 252 miles. This week, he drove m miles. Using m, write an expression for the total number of miles he drove in the two weeks
We add the distance driven:
[B]252 + m[/B]

Last year, Greg biked 524 miles. This year, he biked m miles. Using m , write an expression for the

Last year, Greg biked 524 miles. This year, he biked m miles. Using m , write an expression for the total number of miles he biked.
We add both years to get our algebraic expression of miles biked:
[B]m + 524[/B]

Last year, Maria biked M miles. This year, she biked 390 miles. Using m , write an expression for th

Last year, Maria biked M miles. This year, she biked 390 miles. Using m , write an expression for the total number of miles she biked.
[U]Calculate Total miles biked[/U]
Total miles biked = Last Year + This year
Total miles biked = [B]m + 390[/B]

Last year, the 6th grade had 200 students. This year the number decreased 35% How many students are

Last year, the 6th grade had 200 students. This year the number decreased 35% How many students are in this year's 6th grade class?
[URL='https://www.mathcelebrity.com/percentoff.php?p1=&m=35&p2=200&pl=Calculate']200 decreased by 35%[/URL] is [B]130[/B]

Lebron James scored 288 points in 9 games this season. Assuming he continues to score at this consta

Lebron James scored 288 points in 9 games this season. Assuming he continues to score at this constant rate, write a linear equation that represents the scenario.
288 points / 9 games = 32 points per game
Let g be the number of games Lebron plays. We build an equation for his season score:
Lebron's Season Score = Points per game * number of games
Lebron's Season Score = [B]32g[/B]

Leilani can read 20 pages in 2 minutes. if she can maintain this page, how many pages can she read i

Leilani can read 20 pages in 2 minutes. if she can maintain this page, how many pages can she read in an hour?
We know that 1 hour is 60 minutes.
Let p be the number of pages Leilani can read in 1 hour (60 minutes)
The read rate is constant, so we can build a proportion.
20 pages /2 minutes = p/60
We can cross multiply:
Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2
[SIZE=5][B]Solving for Numerator 2 we get:[/B][/SIZE]
Numerator 2 = Numerator 1 * Denominator 2/Denominator 1
[SIZE=5][B]Evaluating and simplifying using your input values we get:[/B][/SIZE]
p = 20 * 60/ 2
p = 1200/2
p = [B]600[/B]

Leo collects 4 green apples each day for 10 days. How many apples does Leo collect?

Leo collects 4 green apples each day for 10 days. How many apples does Leo collect?
Apples Collected = Apples per day * number of days
Apples Collected = 10 * 4
Apples Collected = [B]40 apples[/B]

Leonard earned $100 from a bonus plus $15 per day (d) at his job this week. Which of the following e

Leonard earned $100 from a bonus plus $15 per day (d) at his job this week. Which of the following expressions best represents Leonards income for the week?
We set up an income function I(d), were d is the number of days Leonard works:
[B]I(d) = 15d + 100
[/B]
Each day, Leonard earns $15. Then we add on the $100 bonus

Leslie has 8 pencils. She has 9 fewer pencils than Michelle. How many pencils does Michelle have?

Let m = the number of pencils Michelle has.
So, Leslie has m - 9 = 8.
Add 9 to both sides:
m = 17. So Michelle has 17 pencils, and Leslie has 8, which is 9 fewer than 17

Let n be an integer. If n^2 is odd, then n is odd

Let n be an integer. If n^2 is odd, then n is odd
Proof by contraposition:
Suppose that n is even. Then we can write n = 2k
n^2 = (2k)^2 = 4k^2 = 2(2k) so it is even
[I]So an odd number can't be the square of an even number. So if an odd number is a square it must be the square of an odd number.[/I]

Let n be the middle number of three consecutive integers

Let n be the middle number of three consecutive integers
This means:
[LIST]
[*]n is the second of three consecutive integers
[*]The first consecutive integer is n - 1
[*]The third consecutive integer is n + 1
[/LIST]
The sum is found by:
n - 1 + n + n + 1
Simplifying, we get:
(n + n + n) + 1 - 1
[B]3n[/B]

Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For

Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What could N be? Is there more than one answer?
For example, for 23 P(23) = 6 and S(23) = 5, but 23 could not be the N that we want since 23 <> 5 + 6
Let t = tens digit and o = ones digit
P(n) = to
S(n) = t + o
P(n) + S(n) = to + t + o
N = 10t + o
Set them equal to each other N = P(N) + S(N)
10t + o = to + t + o
o's cancel, so we have
10t = to + t
Subtract t from each side, we have
9t = to
Divide each side by t
o = 9
So any two-digit number with 9 as the ones digit will work:
[B]{19,29,39,49,59,69,79,89,99}[/B]

Let x be an integer. If x is odd, then x^2 is odd

Let x be an integer. If x is odd, then x^2 is odd
Proof: Let x be an odd number. This means that x = 2n + 1 where n is an integer.
[U]Squaring x, we get:[/U]
x^2 = (2n + 1)^2 = (2n + 1)(2n + 1)
x^2 = 4n^2 + 4n + 1
x^2 = 2(2n^2 + 2n) + 1
2(2n^2 + 2n) is an even number since 2 multiplied by any integer is even
So adding 1 is an odd number
[MEDIA=youtube]GlzV80M33x0[/MEDIA]

Letter Arrangements in a Word

Given a word, this determines the number of unique arrangements of letters in the word.

Liam, a 19th century cowboy, carries an 1847 Colt single action 6 shooter revolver. So proficient is

Liam, a 19th century cowboy, carries an 1847 Colt single action 6 shooter revolver. So proficient is he with this weapon that when he fires all 6 shots in a row, the time between the first bullet and the last is 40 seconds. How long would it take him to fire 4 shots?
We set up a proportion of shots to seconds where s is the number of seconds it takes to fire 4 shots:
6/40 = 4/s
Using our [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=4&den1=40&den2=s&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
s = [B]26.67[/B]

License plate that is made up of 4 letters followed by 2 numbers

License plate that is made up of 4 letters followed by 2 numbers
Using the fundamental rule of counting, we have:
26 possible letters * 26 possible letters * 26 possible letters * 26 possible letters * 10 possible numbers * 10 possible numbers = [B]45,697,600 license plate combinations[/B]

license plate with 4 letter combinations and 3 number combinations

license plate with 4 letter combinations and 3 number combinations
There are 26 total letters and 10 digits [0-9].
We have 26 C 4 * 10 C 3.
[URL='http://www.mathcelebrity.com/permutation.php?num=26&den=4&pl=Combinations']26 C 4[/URL] = 14,950
[URL='http://www.mathcelebrity.com/permutation.php?num=10&den=3&pl=Combinations']10 C 3[/URL] = 120
Total license plate combinations:
14,950 * 120 = [B]1,794,000[/B]

License plates are made using 3 letters followed by 3 digits. How many plates can be made of repetit

License plates are made using 3 letters followed by 3 digits. How many plates can be made of repetition of letters and digits is allowed
We have 26 letters in the alphabet
We have 10 digits [0-9]
The problem asks for the following license plate scenario of Letters (L) and Digits (D)
LLLDDD
The number of plates we can make using L = 26 and D = 10 using the fundamental rule of counting is:
Number of License Plates = 26 * 26 * 26 * 10 * 10 * 10
Number of License Plates = [B]17,576,000[/B]

Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI

Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI with the following monthly billing policies. Each company's monthly billing policy has an initial operating fee and charge per megabyte.
Operating Fee charge per Mb
CIVSIN 29.95 0.14
GOMI 4.95 0.39
(i) Write down a system of equations to model the above situation
(ii) At how many Mb is the monthly cost the same? What is the equal monthly cost of the two plans?
(i) Set up a cost function C(m) for CIVSIN where m is the number of megabytes used:
C(m) = charge per Mb * m + Operating Fee
[B]C(m) = 0.14m + 29.95[/B]
Set up a cost function C(m) for GOMI where m is the number of megabytes used:
C(m) = charge per Mb * m + Operating Fee
[B]C(m) = 0.39m + 4.95
[/B]
(ii) At how many Mb is the monthly cost the same?
Set both cost functions equal to each other:
0.14m + 29.95 = 0.39m + 4.95
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B29.95%3D0.39m%2B4.95&pl=Solve']type this equation into our search engine[/URL] and we get:
m = [B]100[/B]
(ii) What is the equal monthly cost of the two plans?
CIVSIN - We want C(100) from above where m = 100
C(100) = 0.14(100) + 29.95
C(100) = 14 + 29.95
C(100) = [B]43.95[/B]
GOMI - We want C(100) from above where m = 100
C(100) = 0.39(100) + 4.95
C(100) = 39 + 4.95
C(100) = [B]43.95[/B]

Linda estimates that her business is growing at a rate of 6% per year. Her profits is 2002 were $30,

Linda estimates that her business is growing at a rate of 6% per year. Her profits is 2002 were $30,000. To the nearest hundred dollars, estimate her profits for 2011.
Calculate the number of years of appreciation:
Appreciation years = 2011 - 2002
Appreciation years = 9
So we want 30000 to grow for 9 years at 6%. We [URL='https://www.mathcelebrity.com/apprec-percent.php?num=30000togrowfor9yearsat6%.whatisthevalue&pl=Calculate']type this into our search engine[/URL] and we get:
[B]$50,684.37[/B]

Linda takes classes at both Westside Community College and Pinewood Community College. At Westside,

Linda takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit hour, and at Pinewood, class fees are $115 per credit hour. Linda is taking a combined total of 18 credit hours at the two schools. Suppose that she is taking w credit hours at Westside. Write an expression for the combined total dollar amount she paid for her class fees.
Let p be the number of credit hours at Pinewood. We have two equations:
[LIST]
[*]98w for Westside
[*]115p at Pinewood
[*]w + p = 18
[*]Total fees: [B]98w + 115p[/B]
[/LIST]

Lindsey took a total of 8 quizzes over the course of 2 weeks. After attending 5 weeks of school this

Lindsey took a total of 8 quizzes over the course of 2 weeks. After attending 5 weeks of school this quarter, how many quizzes will Lindsey have taken in total? Assume the relationship is directly proportional.
Since the relationship is directly proportional, set up a proportion of quizzes to weeks, where q is the number of quizzes Lindsey will take in 5 weeks:
8/2 = q/5
[URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=q&den1=2&den2=5&propsign=%3D&pl=Calculate+missing+proportion+value']We type this proportion into our search engine[/URL], and we get:
[B]q = 20
[/B]
Another way to look at this is, Lindsey takes 8 quizzes over 2 weeks. This means she takes 4 per week since 8/2 = 4.
So if she takes 4 quizzes per week, then in 5 weeks, she takes 4*5 = 20 quizzes.

Linear Congruential Generator

Using the linear congruential generator algorithm, this generates a list of random numbers based on your inputs

Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend t

Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend the rest on t-shirts that cost $14 each.
Let the number of t-shirts be t. Lisa can spend up to, but not more than 150. We have the following inequality:
14t + 58 <= 150
To solve this inequality, we [URL='https://www.mathcelebrity.com/1unk.php?num=14j%2B58%3C%3D150&pl=Solve']type it in our search engine[/URL] and we get:
t <= 6.57
To round to a whole number, we round down to [B]t = 6 [/B]

Lisa wants to rent a boat and spend less than $52. The boat costs $7 per hour, and Lisa has a discou

Lisa wants to rent a boat and spend less than $52. The boat costs $7 per hour, and Lisa has a discount coupon for $4 off. What are the possible numbers of hours Lisa could rent the boat?
Calculate discounted cost:
Discounted cost = Full Cost - Coupon
Discounted cost = 52 - 7
Discounted cost = 45
Since price equals rate * hours (h), and we want the inequality (less than) we have:
7h < 52
Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=7h%3C52&pl=Show+Interval+Notation']inequality calculator,[/URL] we see that:
[B]h < 7.42[/B]

Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes.

Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes. If the total value of the coins is 2.18, how many of each denomination does she have?
[U]Set up two equations where p is the number of pennies and d is the number of dimes:[/U]
(1) d + p = 47
(2) 0.1d + 0.01p = 2.18
[U]Rearrange (1) into (3) by solving for d[/U]
(3) d = 47 - p
[U]Substitute (3) into (2)[/U]
0.1(47 - p) + 0.01p = 2.18
4.7 - 0.1p + 0.01p = 2.18
[U]Group p terms[/U]
4.7 - 0.09p = 2.18
[U]Add 0.09p to both sides[/U]
0.09p + 2.18 = 4.7
[U]Subtract 2.18 from both sides[/U]
0.09p = 2.52
[U]Divide each side by 0.09[/U]
[B]p = 28[/B]
[U]Now substitute that back into (3)[/U]
d =47 - 28
[B]d = 19[/B]

log5 = 0.699, log2 = 0.301. Use these values to evaluate log40

log5 = 0.699, log2 = 0.301. Use these values to evaluate log40.
One of the logarithmic identities is: log(ab) = log(a) + log(b). Using the numbers 2 and 5, we somehow need to get to 40.
[URL='http://www.mathcelebrity.com/factoriz.php?num=40&pl=Show+Factorization']List factors of 40[/URL].
On the link above, take a look at the bottom where it says prime factorization. We have:
40 = 2 x 2 x 2 x 5
Using our logarithmic identity, we have:
log40 = log(2 x 2 x 2 x 5)
Rewriting this using our identity, we have:
log40 = log2 + log2 + log2 + log5
log40 = 0.301 + 0.301 + 0.301 + 0.699
log40 = [B]1.602[/B]

Logarithms and Natural Logarithms and Eulers Constant (e)

This calculator does the following:

* Takes the Natural Log base e of a number x Ln(x) → log_{e}x

* Raises e to a power of y, e^{y}

* Performs the change of base rule on log_{b}(x)

* Solves equations in the form b^{cx} = d where b, c, and d are constants and x is any variable a-z

* Solves equations in the form ce^{dx}=b where b, c, and d are constants, e is Eulers Constant = 2.71828182846, and x is any variable a-z

* Exponential form to logarithmic form for expressions such as 5^{3} = 125 to logarithmic form

* Logarithmic form to exponential form for expressions such as Log_{5}125 = 3

* Takes the Natural Log base e of a number x Ln(x) → log

* Raises e to a power of y, e

* Performs the change of base rule on log

* Solves equations in the form b

* Solves equations in the form ce

* Exponential form to logarithmic form for expressions such as 5

* Logarithmic form to exponential form for expressions such as Log

Look at this sequence: 53, 53, 40, 40, 27, 27, ... What number should come next?

Look at this sequence: 53, 53, 40, 40, 27, 27, ... What number should come next?
This looks like a sequence where we subtract 13 and then 0, 13 and then 0 from the prior number.
Since the last group of 27 repeated, our next number is found by subtracting 13:
27 - 13 = [B]14[/B]

Lotto Drawing Probability

Given a lotto drawing with a Pick(x) out of (y) total choices, this calculates the probability of winning that lottery picking all (x) correct numbers.

Lucas has nickels,dimes,and quarters in the ratio 1:3:2. If 10 of Lucas coins are quarters, how many

Lucas has nickels,dimes,and quarters in the ratio 1:3:2. If 10 of Lucas coins are quarters, how many nickels and dimes does Lucas have?
1 + 3 + 2 = 6.
Quarters account for 2/6 which is 1/3 of the total coin count. Let x be the total number of coins. We have:
1/3x = 10
Multiply each side by 3
x = 30
We have the following ratios and totals:
[LIST]
[*]Nickels: 1/6 * 30 = [B]5 nickels[/B]
[*]Dimes: 3/6 * 30 = [B]15 dimes[/B]
[*]Quarters: 2/6 * 30 = [B]10 quarters[/B]
[/LIST]

Lucas Numbers

Generates a list of the first 100 Lucas numbers.

M deck of cards . Each deck has 52 cards . The total number of cards

M deck of cards . Each deck has 52 cards . The total number of cards.
[B]52M[/B]

M decreased by the sum of 13 and the number P is less than 12

M decreased by the sum of 13 and the number P is less than 12
The sum of 13 and the number P
13 + P
M decreased by the sum of 13 and the number P
M - (13 + P)
Less than 12 means we set this entire expression less than 12 as an inequality
[B]M - (13 + P) < 12[/B]

m is inversely proportional to the square of p-1 when p=4 m=5 find m when p=6

m is inversely proportional to the square of p-1 when p=4 and m=5. find m when p=6
Inversely proportional means there is a constant k such that:
m = k/(p - 1)^2
When p = 4 and m = 5, we have:
5 = k/(4 - 1)^2
5 = k/3^2
5 = k/9
[U]Cross multiply:[/U]
k = 45
[U]The problems asks for m when p = 6. And we also now know that k = 45. So plug in the numbers:[/U]
m = k/(p - 1)^2
m = 45/(6 - 1)^2
m = 45/5^2
m = 45/25
m = [B]1.8[/B]

Mackenzie baked 12 cookies with 2 scoops of flour. How many scoops of flour does Mackenzie need in o

Mackenzie baked 12 cookies with 2 scoops of flour. How many scoops of flour does Mackenzie need in order to bake 18 cookies? Assume the relationship is directly proportional.
Set up a proportion of cookies to scoops with s as the number of scoops needed for 18 cookies:
12/2 = 18/s
To solve for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=12&num2=18&den1=2&den2=s&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search engine[/URL] and we get:
s = [B]3
[/B]

Maggie earns $10 each hour she works at the pet store and $0.25 for each phone call she answers. Mag

Maggie earns $10 each hour she works at the pet store and $0.25 for each phone call she answers. Maggie answered 60 phone calls and earned $115 last week
Set up an equation where c is the number of phone calls Maggie answers and h is the number of hours Maggie worked:
0.25c + 10h = 115
We're given c = 60, so we have:
0.25(60) + 10h = 115
15 + 10h = 115
We want to solve for h. So we[URL='https://www.mathcelebrity.com/1unk.php?num=15%2B10h%3D115&pl=Solve'] type this equation into our search engine[/URL] and we get:
h = [B]10[/B]

maggie has two job offers. The first job offers to pay her $50 per week and 10 1/2 cents per flier.

maggie has two job offers. The first job offers to pay her $50 per week and 10 1/2 cents per flier. The second job offer will pay only $30 per week but gives 20 cents per flier. Write and solve an equation to find how many fliers must she deliver so that the two offers pay the same per week?
Let the number of fliers be f.
First job:
0.105f + 50
Second job:
20f + 30
Set them equal to each other:
0.105f + 50 = 20f + 30
[URL='https://www.mathcelebrity.com/1unk.php?num=0.105f%2B50%3D20f%2B30&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]f = 1[/B]

Marcela is having a presidential debate watching party with all of her friends, She will be making c

Marcela is having a presidential debate watching party with all of her friends, She will be making chicken wings and hot dogs. Each chicken wing costs $2 to make and each hot dog costs $3. She needs to spend at least $500. Marcela knows that she will make more than 50 chicken wings and hot dogs combined. She also knows that she will make less than 120 chicken wings and less that 100 hot dogs. What are her inequalities?
Let c be the number of chicken wings and h be the number of hot dogs. Set up the given inequalities:
[LIST=1]
[*]c + h > 50 [I]Marcela knows that she will make more than 50 chicken wings and hot dogs combined.[/I]
[*]2c + 3h >= 500 [I]She needs to spend at least $500[/I]
[*]c < 120 [I]She also knows that she will make less than 120 chicken wings[/I]
[*]h < 100 [I]and less that 100 hot dogs[/I]
[/LIST]

Marco puts his coins into stacks. Each stack has 10 coins. He makes 17 stacks of quarters. He makes

Marco puts his coins into stacks. Each stack has 10 coins. He makes 17 stacks of quarters. He makes 11 stacks of dimes. He makes 8 stacks of nickels. How much money does Marco have in his stacks of coins?
[U]Value of Quarters:[/U]
Quarter Value = Value per quarter * coins per stack * number of stacks
Quarter Value = 0.25 * 10 * 17
Quarter Value = 42.5
[U]Value of Dimes:[/U]
Dime Value = Value per dime * coins per stack * number of stacks
Dime Value = 0.10 * 10 * 11
Dime Value = 11
[U]Value of Nickels:[/U]
Nickel Value = Value per nickel * coins per stack * number of stacks
Nickel Value = 0.05 * 10 * 8
Nickel Value = 4
[U]Calculate total value of Marco's coin stacks[/U]
Total value of Marco's coin stacks = Quarter Value + Dime Value + Nickel Value
Total value of Marco's coin stacks = 42.5 + 11 + 4
Total value of Marco's coin stacks = [B]57.5[/B]

Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of

Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of weeks x and the total number of quizzes y. Write your answer as an equation with y first, followed by an equals sign.
Our total quizzes equal 2 times the number of weeks (x):
[B]y = 2x[/B]

Maria bought 7 boxes. A week later half of all her boxes were destroyed in a fire. There are now onl

Maria bought 7 boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start?
[U]Let x be the starting box number. We have:[/U]
(x + 7)/2 = 22
[U]Cross multiply[/U]
x + 7 = 44
[U]Subtract 7 from each side[/U]
[B]x = 37[/B]

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start?
Let the number of boxes Maria started with be b. We're given the following pieces:
[LIST]
[*]She starts with b
[*]She bought 7 boxes. So we add 7 to b: b + 7
[*]If half the boxes were destroyed, she's left with 1/2. So we divide (b + 7)/2
[*]Only 22 boxes left means we set (b + 7)/2 equal to 22
[/LIST]
(b + 7)/2 = 22
Cross multiply:
b + 7 = 22 * 2
b + 7 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B7%3D44&pl=Solve']Type this equation into our search engine[/URL] to solve for b and we get:
b = [B]37[/B]

Maria is saving money to buy a bike that cost 133$. She has 42$ and will save an additional 7 each w

Maria is saving money to buy a bike that cost 133$. She has 42$ and will save an additional 7 each week.
Set up an equation with w as the number of weeks. We want to find w such that:
7w + 42 = 133
[URL='https://www.mathcelebrity.com/1unk.php?num=7w%2B42%3D133&pl=Solve']Typing this equation into our search engine[/URL], we get:
w = [B]13[/B]

Marissa has 24 coins in quarters and nickels. She has 3 dollars. How many of the coins are quarters?

Let n be the number of nickels and q be the number of quarters.
We have two equations:
(1) n + q = 24
(2) 0.05n + 0.25q = 3
Rearrange (1) to solve for n in terms of q for another equation (3)
(3) n = 24 - q
Plug (3) into (2)
0.05(24 - q) + 0.25q = 3
Multiply through:
1.2 - 0.05q + 0.25q = 3
Combine q terms
0.2q + 1.2 = 3
Subtract 1.2 from each side:
0.2q = 1.8
Divide each side by 0.2
[B]q = 9[/B]

Marla wants to rent a bike Green Lake Park has an entrance fee of $8 and charges $2 per hour for bik

Marla wants to rent a bike Green Lake Park has an entrance fee of $8 and charges $2 per hour for bike Oak Park has an entrance fee of $2 and charges $5 per hour for bike rentals she wants to know how many hours are friend will make the costs equal
[U]Green Lake Park: Set up the cost function C(h) where h is the number of hours[/U]
C(h) = Hourly Rental Rate * h + Entrance Fee
C(h) = 2h + 8
[U]Oak Park: Set up the cost function C(h) where h is the number of hours[/U]
C(h) = Hourly Rental Rate * h + Entrance Fee
C(h) = 5h + 2
[U]Marla wants to know how many hours make the cost equal, so we set Green Lake Park's cost function equal to Oak Parks's cost function:[/U]
2h + 8 = 5h + 2
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2h%2B8%3D5h%2B2&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]2[/B]

Mary owns a store that sells computers. Her profit in dollars is represented by the function P(x) =

Mary owns a store that sells computers. Her profit in dollars is represented by the function P(x) = x^3 - 22x^2 - 240x, where x is the number of computers sold. Mary hopes to make a profit of at least $10,000 by the time she sells 36 computers. Explain whether Mary will meet her goal. Justify your reasoning.
Calculate P(10):
P(10) = 10^3 - 22(10)^2 - 240(10)
P(10) = 1000 - 2200 - 2400
P(10) = -3600
Mary will [B]not[/B] meet her goal of making a profit of at least $10,000 when she sells 36 computers because her profit is in the negative.

Mary went bowling on the weekend. Each game cost $2.50, and the shoe rental $2.00. She spent $14.50

Mary went bowling on the weekend. Each game cost $2.50, and the shoe rental $2.00. She spent $14.50 total. How many games did she bowl?
Set up the equation where g is the number of games. We add the shoe rental fee to the cost per games
2.5g + 2 = 14.50
To solve for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5g%2B2%3D14.50&pl=Solve']type this equation into our search engine[/URL] and we get:
g = [B]5[/B]

Math Problem Solving (Help Please)

Volume of rectangular prism is:
V = lwh
Plugging in the numbers you gave:
195 = (6)(5)h
195 = 30h
Divide each side by 30
h = 6.5
6.5 feet is 6 feet, 6 inches. This is 2 inches more than your actor, so [B]yes[/B], he will fit in the box standing up.

Matt has $100 dollars in a checking account and deposits $20 per month. Ben has $80 in a checking ac

Matt has $100 dollars in a checking account and deposits $20 per month. Ben has $80 in a checking account and deposits $30 per month. Will the accounts ever be the same balance? explain
Set up the Balance account B(m), where m is the number of months since the deposit.
Matt:
B(m) = 20m + 100
Ben:
B(m) = 80 + 30m
Set both balance equations equal to each other to see if they ever have the same balance:
20m + 100 = 80 + 30m
To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=20m%2B100%3D80%2B30m&pl=Solve']we type this equation into our search engine[/URL] and we get:
m = [B]2
So yes, they will have the same balance at m = 2[/B]

Matthew's pay increases by 20% each month. If his first pay is $450, determine the amount of his pay

Matthew's pay increases by 20% each month. If his first pay is $450, determine the amount of his pay in month 5.
Let me be the number of months. We have a pay functionalists P(m) as:
P(m) = Initial Pay * (1 + Increase %/100)^m
With m = 5, initial pay = 450, and Increase % = 20, we have
P(5) = 450 * (1.2)^5
P(5) = 450 * 2.48832
P(5) = [B]1,119.74[/B]

Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many

Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many weeks will megan and connor have saved the same amount
[U]Set up the Balance function B(w) where w is the number of weeks for Megan:[/U]
B(w) = savings per week * w + Current Balance
B(w) = 5.50w + 50
[U]Set up the Balance function B(w) where w is the number of weeks for Connor:[/U]
B(w) = savings per week * w + Current Balance
B(w) = 7.75w + 18.50
The problem asks for w when both B(w) are equal. So we set both B(w) equations equal to each other:
5.50w + 50 = 7.75w + 18.50
To solve this equation for w, we[URL='https://www.mathcelebrity.com/1unk.php?num=5.50w%2B50%3D7.75w%2B18.50&pl=Solve'] type it in our search engine[/URL] and we get:
w = [B]14[/B]

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she c

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she charges $53 for each lawn, how many lawns must she service to make a profit of at $800 a month?
Melissa has a fixed cost of $264 per month in fuel. No variable cost is given. Our cost function is:
C(x) = Fixed Cost + Variable Cost. With variable cost of 0, we have:
C(x) = 264
The revenue per lawn is 53. So R(x) = 53x where x is the number of lawns.
Now, profit is Revenue - Cost. Our profit function is:
P(x) = 53x - 264
To make a profit of $800 per month, we set P(x) = 800.
53x - 264 = 800
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=53x-264%3D800&pl=Solve']equation solver[/URL], we get:
[B]x ~ 21 lawns[/B]

Melissa’s flower shop got a shipment of 252 tuilps. She wants to make bouquets of 12 tulips each. Ho

Melissa’s flower shop got a shipment of 252 tuilps. She wants to make bouquets of 12 tulips each. How many bouquets can Melissa make?
Number of bouquets = Total tulips in shipment / tulips per bouquet
Number of bouquets = 252/12
Number of bouquets = [B]21[/B]

Miguel bought 8 boxes of chocolate. Each box cost 6.36. How much did he spend

Miguel bought 8 boxes of chocolate. Each box cost 6.36. How much did he spend?
Total spend = Number of boxes * cost per box
Total spend = 8 * 6.36
Total spend = [B]$50.88[/B]

Miguel has $80 in his bank and saves $2 a week. Jesse has $30 in his bank but saves $7 a week. In ho

Miguel has $80 in his bank and saves $2 a week. Jesse has $30 in his bank but saves $7 a week. In how many weeks will Jesse have more in his bank than Miguel?
[U]Set up the Bank value B(w) for Miguel where w is the number of weeks[/U]
B(w) = Savings Per week * w + Current Bank Balance
B(w) = 2w + 80
[U]Set up the Bank value B(w) for Jesse where w is the number of weeks[/U]
B(w) = Savings Per week * w + Current Bank Balance
B(w) = 7w + 30
The problem asks when Jesse's account will be more than Miguel's. So we set up an inequality where:
7w + 30 > 2w + 80
To solve this inequality, we [URL='https://www.mathcelebrity.com/1unk.php?num=7w%2B30%3E2w%2B80&pl=Solve']type it in our search engine[/URL] and we get:
[B]w > 10[/B]

Mike cut 2 acres of grass in 30 minutes on his tractor. Which proportion would determine how many ac

Mike cut 2 acres of grass in 30 minutes on his tractor. Which proportion would determine how many acres of grass Mike cut in 60 minutes?
Let a be the number of acres of grass cut by Mike in 60 minutes. We have the following proportion:
2/30 = a/60
[URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=a&den1=30&den2=60&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this problem into our search engine[/URL], we get [B]a = 4[/B].

mike went to canalside with $40 to spend. he rented skates for $10 and paid $3 per hour to skate.wha

mike went to canalside with $40 to spend. he rented skates for $10 and paid $3 per hour to skate.what is the greatest number of hours Mike could have skated?
Let h be the number of hours of skating. We have the cost function C(h):
C(h) = Hourly skating rate * h + rental fee
C(h) = 3h + 10
The problem asks for h when C(h) = 40:
3h + 10 = 40
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=3h%2B10%3D40&pl=Solve']type it in our search engine[/URL] and we get:
h = [B]10[/B]

Mike writes a book and gets 15% royalty of total sales. He sells 50,000 books at a cost of $35 per b

Mike writes a book and gets 15% royalty of total sales. He sells 50,000 books at a cost of $35 per book. What is the royalty he receives? Remember to put the $ symbol in your answer. For example, if your answer is 10 dollars, write $10 in the answer box.
[U]Calculate total sales:[/U]
Total Sales = Number of Books * Price per book
Total Sales = 50,000 * $35
Total Sales = $1,750,000
[U]Now calculate Mike's royalties:[/U]
Royalties = Total Sales * Royalty Percent
Royalties = $1,750,000 * 15%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=15&den1=1750000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Royalties[/URL] = [B]$262,500[/B]

Milan plans to watch 2 movies each month. Write an equation to represent the total number of movies

Milan plans to watch 2 movies each month. Write an equation to represent the total number of movies n that he will watch in m months.
Number of movies equals movies per month times the number of months. So we have:
[B]n = 2m[/B]

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opp

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent's serves. Assume her opponent serves 8 times. Show all work. Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution.
a) What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?
b) Find the probability that that she returns at least 1 of the 8 serves from her opponent.
(c) How many serves can she expect to return?
a) [B]n = 8
p = 0.2[/B]
q = 1 - p
q = 1 - 0.2
[B]q = 0.8
[/B]
b) [B]0.4967[/B] on our [URL='http://www.mathcelebrity.com/binomial.php?n=+8&p=0.2&k=1&t=+5&pl=P%28X+>+k%29']binomial calculator[/URL]
c) np = 8(0.2) = 1.6 ~ [B]2[/B] using the link above

Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake troy had 1/4 of

Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake troy had 1/4 of the total cake. Write an equation to determine how many pieces of cake (c) that were in total
Let c be the total number of pieces of cake. Let m be the number of pieces Mindy ate. Let t be the number of pieces Troy ate. We have the following given equations:
[LIST]
[*]m + t = 9
[*]m = 3
[*]t = 1/4c
[/LIST]
Combining (2) and (3) into (1), we have:
3 + 1/4c = 9
Subtract 3 from each side:
1/4c = 6
Cross multiply:
[B]c = 24[/B]

Morse Code Translator

Given a phrase with letters, numbers, and most punctuation symbols, the calculator will perform the following duties:

1) Translate that phrase to Morse Code.

2) Translate the Morse Code to a Dit-Dah message

3) Calculate the number of dots in the message

4) Calculate the number of dashes in the message

This also translates__from__ Morse Code back to English.

1) Translate that phrase to Morse Code.

2) Translate the Morse Code to a Dit-Dah message

3) Calculate the number of dots in the message

4) Calculate the number of dashes in the message

This also translates

Mr. Chris’s new app “Tick-Tock” is the hottest thing to hit the app store since...ever. It costs $5

Mr. Chris’s new app “Tick-Tock” is the hottest thing to hit the app store since...ever. It costs $5 to buy the app and then $2.99 for each month that you subscribe (a bargain!). How much would it cost to use the app for one year? Write an equation to model this using the variable “m” to represent the number of months that you use the app.
Set up the cost function C(m) where m is the number of months you subscribe:
C(m) = Monthly Subscription Fee * months + Purchase fee
[B]C(m) = 2.99m + 5[/B]

Mr. Crimmins bought 15 apples and 15 oranges. Each apple cost $1.00, each orange cost $1.50. How muc

Mr. Crimmins bought 15 apples and 15 oranges. Each apple cost $1.00, each orange cost $1.50. How much more did he spend on oranges than apples?
[U]Calculate apple spend:[/U]
Apple Spend = Apple Cost * Number of Apples
Apple Spend = $1.00 * 15
Apple Spend =[B] [/B]$15
[B][/B]
[U]Calculate apple spend:[/U]
Orange Spend = Orange Cost * Number of Oranges
Orange Spend = $1.50 * 15
Orange Spend = $22.50
[B][/B]
[U]Calculate the additional amount spent on oranges over apples:[/U]
Additional Orange Spend = Orange Spend - Apple Spend
Additional Orange Spend = $22.50 - $15.00
Additional Orange Spend = [B]$7.50[/B]

Mr. Demerath has a large collection of Hawaiian shirts. He currently has 42 Hawaiian shirts. He gets

Mr. Demerath has a large collection of Hawaiian shirts. He currently has 42 Hawaiian shirts. He gets 2 more every month. After how many months will Mr. Demerath have at least 65 Hawaiian shirts?
We set up the function H(m) where m is the number of months that goes by. Mr. Demerath's shirts are found by:
H(m) = 2m + 42
The problem asks for m when H(m) = 65. So we set H(m) = 65:
2m + 42 = 65
To solve this equation for m, we[URL='https://www.mathcelebrity.com/1unk.php?num=2m%2B42%3D65&pl=Solve'] type it in our search engine [/URL]and we get:
m = [B]11.5[/B]

Mr. Elk is secretly a huge fan of Billie Eilish, and is saving up for front row seats. He puts $250

Mr. Elk is secretly a huge fan of Billie Eilish, and is saving up for front row seats. He puts $250 in the bank that has an interest rate of 8% compounded daily. After 4 years, Billie is finally hitting up NJ on her tour. How much money does Mr. Elk have in the bank? (rounded to the nearest cent) *
4 years = 365*4 days
4 years = 1,460 days.
Using this number of compounding periods, we [URL='https://www.mathcelebrity.com/compoundint.php?bal=250&nval=1460&int=8&pl=Daily']plug this into our compound interest calculator[/URL] to get:
[B]$344.27[/B]

Mr. Wilson wants to park his carin a parking garage that charges 3 per hour along with a flat fee of

Mr. Wilson wants to park his carin a parking garage that charges 3 per hour along with a flat fee of 6. If Mr. Wilson paid 54 to park in the garage, for how many hours did he park there?
[U]Set up an equation, where f is the flat fee, and h is the number of hours parked:[/U]
3h + f = 54
[U]Substitute f = 6 into the equation:[/U]
3h + 6 = 54
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3h%2B6%3D54&pl=Solve']equation solver[/URL], we get[/U]
[B]h = 16[/B]

Mrs. Evans has 120 crayons and 30 pieces of paper to give her students. What is the largest number o

Mrs. Evans has 120 crayons and 30 pieces of paper to give her students. What is the largest number of students she can have her class so that each student gets an equal number of crayons and equal number of paper?
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=30&num2=120&num3=&pl=GCF+and+LCM']Using our GCF calculator for the GCF(30, 120)[/URL], we get 30.
So 30 people get the following:
[B]30/30 = 1 piece of paper
120/30 = 4 crayons[/B]

Mrs. Lowe charges $45 an hour with a $10 flat fee for tutoring. Mrs. Smith charges $40 an hour wit

Mrs. Lowe charges $45 an hour with a $10 flat fee for tutoring. Mrs. Smith charges $40 an hour with a $15 flat fee to tutor. Write an equation that represents the situation when the cost is the same to be tutored by Mrs. Lowe and Mrs. Smith.
[U]Set up cost equation for Mrs. Lowe where h is the number of hours tutored:[/U]
Cost = Hourly Rate * number of hours + flat fee
Cost = 45h + 10
[U]Set up cost equation for Mrs. Smith where h is the number of hours tutored:[/U]
Cost = Hourly Rate * number of hours + flat fee
Cost = 40h + 15
[U]Set both cost equations equal to each other:[/U]
45h + 10 = 40h + 15 <-- This is our equation
To solve for h if the problem asks, we [URL='https://www.mathcelebrity.com/1unk.php?num=45h%2B10%3D40h%2B15&pl=Solve']type this equation into our search engine[/URL] and we get:
h = 1

Mrs. Taylor is making identical costumes for the dancers in the dance club. She uses 126 pink ribbon

Mrs. Taylor is making identical costumes for the dancers in the dance club. She uses 126 pink ribbons and 108 yellow ribbons.
a) What is the maximum possible number of costumes she can make?
b) How many pink and how many yellow ribbons are on each costume?
a), we want the greatest common factor (GCF) of 108 and 126. [URL='https://www.mathcelebrity.com/gcflcm.php?num1=108&num2=126&num3=&pl=GCF+and+LCM']Using our GCF calculator[/URL] we get:
[B]a) 18 costumes
[/B]
b)
Pink Ribbons per costume = Total Pink Ribbons / GCF in question a
Pink Ribbons per costume = 126/18
Pink Ribbons per costume = [B]7[/B]
[B][/B]
Yellow Ribbons per costume = Total Yellow Ribbons / GCF in question a
Yellow Ribbons per costume = 108/18
Yellow Ribbons per costume = [B]6[/B]

Multiplicative Identity Property

Demonstrates the Multiplicative Identity property using a number.
Numerical Properties

Multiplicative Inverse Property

Demonstrates the Multiplicative Inverse property using a number.
Numerical Properties

multiply a number by 4 and then subtract the answer from 30

multiply a number by 4 and then subtract the answer from 30
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Multiply this number by 4:
4x
Subtract the answer from 30:
[B]30 - 4x[/B]

Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and su

Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and subtracting 4. Find the number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
multiply a number by 6 and subtract 6:
6x - 6
Multiply a number by 3 and subtract 4:
3x - 4
The phrase [I]gives the same result[/I] means an equation. So we set 6x - 6 equal to 3x - 4
6x - 6 = 3x - 4
To solve this equation for x, we type it in our search engine and we get:
x = [B]2/3[/B]

Multiplying a number by 6 is equal to the number increased by 9

Multiplying a number by 6 is equal to the number increased by 9.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Multiply it by 6 --> 6x
We set this equal to the same number increased by 9. Increased by means we add:
[B]6x = x + 9 <-- This is our algebraic expression
[/B]
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x%3Dx%2B9&pl=Solve']type it into the search engine [/URL]and get x = 1.8.

Murray makes $12.74 per hour. How much does he earn in 38 hours?

Murray makes $12.74 per hour. How much does he earn in 38 hours?
[U]Calculate Earnings:[/U]
Earnings = Hourly Rate * Number of hours worked
Earnings = $12.74 * 38
Earnings = [B]$484.12[/B]

N-Grams

Takes a phrase and displays chracter unigrams, character bigrams, character trigrams, and character n-grams as well as word unigrams, word bigrams, word trigrams, and word n-grams. (ngrams)

Also performs frequency analysis (number of instances of each letter)

Also performs frequency analysis (number of instances of each letter)

Nancy shot a 16 on 4 holes of golf. At this rate, what can she expect her score to be if she plays 1

Nancy shot a 16 on 4 holes of golf. At this rate, what can she expect her score to be if she plays 18 holes? Round to the nearest whole number
Set up a proportion of score to holes of golf where s is the score for 18 holes:
16/4 = s/18
To solve this proportion for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=s&den1=4&den2=18&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
s = [B]72[/B]

Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and i

Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and is spending $15 a week. [I]When will they both have the same amount of money in the bank?[/I]
[I][/I]
Set up the Account equation A(w) where w is the number of weeks that pass.
Nancy (we add since savings means she accumulates [B]more[/B]):
A(w) = 25w + 435
Shane (we subtract since spending means he loses [B]more[/B]):
A(w) = 875 - 15w
Set both A(w) equations equal to each other to since we want to see what w is when the account are equal:
25w + 435 = 875 - 15w
[URL='https://www.mathcelebrity.com/1unk.php?num=25w%2B435%3D875-15w&pl=Solve']Type this equation into our search engine to solve for w[/URL] and we get:
w =[B] 11[/B]

nandita earned $224 last month. she earned $28 by selling cards at a craft fair and the rest of the

nandita earned $224 last month. she earned $28 by selling cards at a craft fair and the rest of the money by babysitting. Complete an equation that models the situation and can be used to determine x, the number of dollars nandita earned last month by babysitting.
We know that:
Babysitting + Card Sales = Total earnings
Set up the equation where x is the dollars earned from babysitting:
[B]x + 28 = 224[/B]
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B28%3D224&pl=Solve']type it in our math engine[/URL] and we get:
x = [B]196[/B]

Natural Logarithm Table

Generates a natural logarithm table for the first (n) numbers rounded to (r) digits

Natural Numbers

Shows a set amount of natural numbers and cumulative sum

natural numbers that are factors of 16

natural numbers that are factors of 16
Natural numbers are positive integers starting at 1.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
Of these, [URL='https://www.mathcelebrity.com/factoriz.php?num=16&pl=Show+Factorization']the only factors of 16[/URL] are:
{[B]1, 2, 4, 8, 16}[/B]

Need Help on this problem

What do you want to do with this number set? Express it as representation of integers?

Nine less than a number is no more than 8 and no less than 3

Nine less than a number is no more than 8 and no less than 3
A number is denoted as an arbitrary variable, let's call it x.
We have a double inequality:
[LIST=1]
[*]No more than 8 means less than or equal to 8
[*]No less than 3 means greater than or equal to 3
[/LIST]
[B]3 <= x <= 8[/B]

Nine times the sum of a number and 6

Nine times the sum of a number and 6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 6 means we add 6 to x:
x + 6
9 times the sum:
[B]9(x + 6)[/B]

Nine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in s

Nine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in size. What is the total area of the field?
Area of each plot is 5x5 = 25 square feet.
Total area = Area per plot * number of plots
Total area = 25 sq ft * 9
Total area = [B]225 sq ft[/B]

Ning prepared 16 kilograms of dough after working 4 hours. How many hours did Ning work if he prepar

Ning prepared 16 kilograms of dough after working 4 hours. How many hours did Ning work if he prepared 28 kilograms of dough? Assume the relationship is directly proportional.
Set up a proportion of kilograms of dough to working hours. We have:
16/4 = 28/h where h is the number of hours worked.
Typing this in our [URL='http://www.mathcelebrity.com/prop.php?num1=16&num2=28&den1=4&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]h = 7[/B].

Nonagonal Number

This calculator determines the nth nonagonal number

Notebooks cost $1.39 each. What are the possible numbers of notebooks that can be purchased with $10

Notebooks cost $1.39 each. What are the possible numbers of notebooks that can be purchased with $10?
Let n be the number of notebooks you can purchase. We have the following inequality:
1.39n <= 10
Divide each side by 1.39
n <= 7.194
We want whole notebooks, we cannot buy fractions of notebooks, so we have:
n <= 7
The question asks for the possible numbers of notebooks we can buy. This implies we buy at least 1, but our inequality says not more than 7. So our number set is:
[B]N = {1, 2, 3, 4, 5, 6, 7}[/B]

Number Bonds

Adds or subtracts 2 numbers and using grouping by 10 or 100. Also called number bonds or addition facts. Multiplies two numbers using tape diagrams.

Number Line

Counts from a point going left and right on a number line

Number Line Midpoint

Calculates a midpoint between 2 points on a number line or finds the second endpoint if one endpoint and midpoint are given.

Number of cents in q quarters is 275

Number of cents in q quarters is 275
Each quarter makes 25 cents. We write this as 0.25q.
Now set this equal to 275
0.25q = 275
Typing this [URL='http://www.mathcelebrity.com/1unk.php?num=0.25q%3D275&pl=Solve']equation in the search engine[/URL], we get [B]q = 1,100[/B].

Number Property

This calculator determines if an integer you entered has any of the following properties:

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

Numbers Word Problems

Solves various basic math and algebra word problems with numbers

n^2+n = odd

n^2+n = odd
Factor n^2+n:
n(n + 1)
We have one of two scenarios:
[LIST=1]
[*]If n is odd, then n + 1 is even. The product of an odd and even number is an even number
[*]If n is even, then n + 1 is odd. The product of an even and odd number is an even number
[/LIST]

n^2-n = even

n^2-n = even
Factor n^2-n:
n(n - 1)
We have one of two scenarios:
[LIST=1]
[*]If n is odd, then n - 1 is even. The product of an odd and even number is an even number
[*]If n is even, then n - 1 is odd. The product of an even and odd number is an even number
[/LIST]

Oceanside Bike Rental Shop charges $15.00 plus $9.00 per hour for renting a bike. Dan paid $51.00 to

Oceanside Bike Rental Shop charges $15.00 plus $9.00 per hour for renting a bike. Dan paid $51.00 to rent a bike. How many hours was he hiking for?
Set up the cost equation C(h) where h is the number of hours needed to rent the bike:
C(h) = Cost per hour * h + rental charge
Using our given numbers in the problem, we have:
C(h) = 9h + 15
The problem asks for h, when C(h) = 51.
9h + 15 = 51
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=9h%2B15%3D51&pl=Solve']plug this equation into our search engine[/URL] and we get:
h = [B]4[/B]

Oceanside Bike Rental Shop charges 16 dollars plus 6 dollars an hour for renting a bike. Mary paid 5

Oceanside Bike Rental Shop charges 16 dollars plus 6 dollars an hour for renting a bike. Mary paid 58 dollars to rent a bike. How many hours did she pay to have the bike checked out ?
Set up the cost function C(h) where h is the number of hours you rent the bike:
C(h) = Hourly rental cost * h + initial rental charge
C(h) = 6h + 16
Now the problem asks for h when C(h) = 58, so we set C(h) = 58:
6h + 16 = 58
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=6h%2B16%3D58&pl=Solve']type it in our math engine[/URL] and we get:
h = [B]7 hours[/B]

Octagonal Number

This calculator determines the nth octagonal number

Odd Numbers

Shows a set amount of odd numbers and cumulative sum

Of the 20 boats at the Mariana, 10 were from Massachusetts. What is the probability that a randomly

Of the 20 boats at the Mariana, 10 were from Massachusetts. What is the probability that a randomly selected boat will be from Massachusetts?
P(Boat from Massachusetts) = Number of Massachusetts boats / Total Boats at the Mariana
P(Boat from Massachusetts) = 10/20
[URL='https://www.mathcelebrity.com/fraction.php?frac1=10%2F20&frac2=3%2F8&pl=Simplify']Simplifying this fraction, we get[/URL]:
P(Boat from Massachusetts) = [B]1/2[/B]

Olga wrote all the natural numbers from 1 to k. Including 1 and k. How many numbers did she write?

Olga wrote all the natural numbers from 1 to k. Including 1 and k. How many numbers did she write?
The formula for the number of numbers including A to B is:
B - A + 1
With A = 1 and B = k, we have:
k - 1 + 1
[B]k[/B]

Oliver earns $50 per day plus $7.50 for each package he delivers. If his paycheck for the first day

Oliver earns $50 per day plus $7.50 for each package he delivers. If his paycheck for the first day was $140, how many packages did he deliver that day?
His total earnings per day are the Flat Fee of $50 plus $7.50 per package delivered. We have:
50 + 7.50p = 140 where p = the number of packages delivered
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=50%2B7.50p%3D140&pl=Solve']equation solver[/URL], we have:
[B]p = 12[/B]

Omar mows lawns for $9.25 an hour. He spends $7.50 on gas for the mower. How much does he make if he

Omar mows lawns for $9.25 an hour. He spends $7.50 on gas for the mower. How much does he make if he works h hours?
His revenue R(h) where h is the number of hours is denoted by:
R(h) = Hourly Rate * h - Gas cost
[B]R(h) = 9.25h - 7.50[/B]

Omar mows lawns for $9.25 per hour. He spends $7.50 on gas for the mower. How much does he make if h

Omar mows lawns for $9.25 per hour. He spends $7.50 on gas for the mower. How much does he make if he works h hours?
We have the following profit equation:
Profit = Revenue - Cost:
Revenue = Hourly rate * number of hours
[B]9.25h - 7.50[/B]

On a Friday evening a pizza shop had orders for 4 pepperoni, 97 vegetable, and 335 cheese pizzas. If

On a Friday evening a pizza shop had orders for 4 pepperoni, 97 vegetable, and 335 cheese pizzas. If the 4 cooks each made an equal number of pizzas, how many pizzas did each cook make?
Total Pizzas Made = 4 pepperoni + 97 vegetable + 335 cheese
Total Pizzas Made = 436
Equal number of pizzas per cook = 436 pizzas / 4 cooks
Equal number of pizzas per cook = [B]109[/B]

On a Math test, 12 students earned an A. This number is exactly 25% of the total number of students

On a Math test, 12 students earned an A. This number is exactly 25% of the total number of students in the class. How many students are in the class?
Let the total number of students be s. Since 25% is 0.25 as a decimal, We have an equation:
0.25s = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%3D12&pl=Solve']Type this equation into our search engine[/URL], and we get:
s = [B]48[/B]

On a particular road map, 1/2 inch represents 18 miles. About how many miles apart are 2 towns that

On a particular road map, 1/2 inch represents 18 miles. About how many miles apart are 2 towns that are 2 1/2 inches apart on this map?
A) 18
B) 22 1/2
C) 36
D) 45
E) 90
Set up a proportion of inches to miles where m is the number of miles for 2 1/2 inches. Note: 1/2 = 0.5 and 2 1/2 = 2.5
0.5/18 = 2.5/m
[URL='https://www.mathcelebrity.com/prop.php?num1=0.5&num2=2.5&den1=18&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into the search engine[/URL], we get:
[B]m = 90 Answer E[/B]

On Monday 208 student went on a trip to the zoo . All 5 buses were filled and 8 student had to trave

On Monday 208 student went on a trip to the zoo . All 5 buses were filled and 8 student had to travel in car . How many student were in each bus?
Calculate the number of students who traveled by bus:
Total bus Students = Total Students - Total Car Students
Total bus Students = 208 - 8
Total bus Students = 200
Figure how the students per bus:
Students per bus = Total Bus Students / Number of Filled Busses
Students per bus = 200/5
Students per bus = [B]40[/B]

On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday

On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday they paid 15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel
Let the number of cups of coffee be c
Let the number of bagels be b.
Since cost = Price * Quantity, we're given two equations:
[LIST=1]
[*]7b + 4c = 8.77
[*]14b + 8c = 15.80
[/LIST]
We have a system of equations. We can solve this 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer
[LIST]
[*]The system is inconsistent. Therefore, we have no answer.
[/LIST]

On the first day of school each student in the class of 26 will bring 4 writing books and 2 maths bo

On the first day of school each student in the class of 26 will bring 4 writing books and 2 maths books. How many books will they have altogether?
Each student has 4 books plus 2 math books = 6 total books per student
Calculate total books
Total Books = Number of students * books per student
Total Books = 26 * 6
Total Books = [B]156[/B]

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a total of $82. The school took in $67 on the second day by selling 8 senior citizen tickets And 5 child tickets. What is the price of each ticket?
Let the number of child tickets be c
Let the number of senior citizen tickets be s
We're given two equations:
[LIST=1]
[*]10c + 3s = 82
[*]5c + 8s = 67
[/LIST]
We have a system of simultaneous equations. We can solve it using any one of 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]c = 7[/B]
[*][B]s = 4[/B]
[/LIST]

One and one third less x

One and one-third can be written as 4/3.
Less x means minus x, or subtract x.
4/3 - x
Or in mixed number notation:
1 & 1/3 - x

One fifth of the square of a number

One fifth of the square of a number
We have an algebraic expression. Let's break this into parts.
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The square of a number means we raise it to the power of 2. So we have x^2
[*]One-fifth means we have a fraction, where we divide our x^2 in Step 2 by 5. So we get our final answer below:
[/LIST]
[B]x^2/5[/B]

One number exceeds another by 15. The sum of the numbers is 51. What are these numbers

One number exceeds another by 15. The sum of the numbers is 51. What are these numbers?
Let the first number be x, and the second number be y. We're given two equations:
[LIST=1]
[*]x = y + 15
[*]x + y = 51
[/LIST]
Plug (1) into (2)
(y + 15) + y = 51
Combine like terms:
2y + 15 = 51
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B15%3D51&pl=Solve']Plug this equation into the search engine[/URL] and we get:
[B]y = 18[/B]
Now plug this into (1) to get:
x = 18 + 15
[B]x = 33[/B]

One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a c

One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a comma to separate your answers.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x = 1/4y
[*]x + y = 25
[/LIST]
Substitute (1) into (2)
1/4y + y = 25
Since 1/4 = 0.25, we have:
0.25y + y = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25y%2By%3D25&pl=Solve']Type this equation into the search engine[/URL] to get:
[B]y = 20
[/B]
Now, substitute this into (1) to solve for x:
x = 1/4y
x = 1/4(20)
[B]x = 5
[/B]
The problem asks us to separate the answers by a comma. So we write this as:
[B](x, y) = (5, 20)[/B]

One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers.

One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers.
Let the two numbers be x and y. We're given:
[LIST=1]
[*]x = 1/5y
[*]x + y = 18
[/LIST]
Substitute (1) into (2):
1/5y + y = 18
1/5 = 0.2, so we have:
1.2y = 18
[URL='https://www.mathcelebrity.com/1unk.php?num=1.2y%3D18&pl=Solve']Type 1.2y = 18 into the search engine[/URL], and we get [B]y = 15[/B].
Which means from equation (1) that:
x = 15/5
[B]x = 3
[/B]
Our final answer is [B](x, y) = (3, 15)[/B]

One number is 3 times another. Their sum is 44.

One number is 3 times another. Their sum is 44.
Let the first number be x, and the second number be y. We're given:
[LIST=1]
[*]x = 3y
[*]x + y = 44
[/LIST]
Substitute (1) into (2):
3y + y = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=3y%2By%3D44&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]y = 11[/B]
Plug this into equation (1):
x = 3(11)
[B]x = 33[/B]

one number is 3 times as large as another. Their sum is 48. Find the numbers

one number is 3 times as large as another. Their sum is 48. Find the numbers
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x = 3y
[*]x + y = 48
[/LIST]
Substitute equation (1) into equation (2):
3y + y = 48
To solve for y, [URL='https://www.mathcelebrity.com/1unk.php?num=3y%2By%3D48&pl=Solve']we type this equation into the search engine[/URL] and we get:
[B]y = 12[/B]
Now, plug y = 12 into equation (1) to solve for x:
x = 3(12)
[B]x = 36[/B]

One number is 4 times the other number

Let one number be x, and the other number be y
[B]x = 4y[/B]

One number is 8 times another number. The numbers are both positive and have a difference of 70.

One number is 8 times another number. The numbers are both positive and have a difference of 70.
Let the first number be x, the second number be y. We're given:
[LIST=1]
[*]x = 8y
[*]x - y = 70
[/LIST]
Substitute(1) into (2)
8y - y = 70
[URL='https://www.mathcelebrity.com/1unk.php?num=8y-y%3D70&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]y = 10[/B] <-- This is the smaller number
Plug this into Equation (1), we get:
x = 8(10)
[B]x = 80 [/B] <-- This is the larger number

One number is equal to the square of another. Find the numbers if both are positive and their sum is

One number is equal to the square of another. Find the numbers if both are positive and their sum is 650
Let the number be n. Then the square is n^2. We're given:
n^2 + n = 650
Subtract 650 from each side:
n^2 + n - 650 = 0
We have a quadratic equation. [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-650%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']We type this into our search engine[/URL] and we get:
n = 25 and n = -26
Since the equation asks for a positive solution, we use [B]n = 25[/B] as our first solution.
the second solution is 25^2 = [B]625[/B]

one number is twice a second number. the sum of those numbers is 45

one number is twice a second number. the sum of those numbers is 45.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x = 2y
[*]x + y = 45
[/LIST]
Substitute Equation (1) into Equation (2):
2y + y = 45
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2By%3D45&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 15[/B]
Plug this into equation (1) to solve for x, and we get:
x = 2(15)
[B]x = 30[/B]

One positive number is one-fifth of another number. The difference between the two numbers is 192, f

One positive number is one-fifth of another number. The difference between the two numbers is 192, find the numbers.
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*]x = y/5
[*]x + y = 192
[/LIST]
Substitute equation 1 into equation 2:
y/5 + y = 192
Since 1 equals 5/5, we rewrite our equation like this:
y/5 = 5y/5 = 192
We have fractions with like denominators, so we add the numerators:
(1 + 5)y/5 = 192
6y/5 = 192
[URL='https://www.mathcelebrity.com/prop.php?num1=6y&num2=192&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Type this equation into our search engine[/URL], and we get:
[B]y = 160[/B]
Substitute this value into equation 1:
x = 160/5
x = [B]32[/B]

One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels.

One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels.
Set up our equation where b is the number of total bagels
72 = b/3
Multiply each side by 3
[B]b = 216[/B]

one-fifth of forty-five

one-fifth of forty-five
one-fifth is 1/4
forty-five is 45
When you see a fraction then the word of and then a number, it means you multiply:
1/5 * 45
45/5
[B]9[/B]

Opposite Numbers

Given a positive or negative integer (n), this calculates the opposite number of n

Orange Theory is currently offering a deal where you can buy a fitness pass for $100 and then each c

Orange Theory is currently offering a deal where you can buy a fitness pass for $100 and then each class is $13, otherwise it is $18 for each class. After how many classes is the total cost with the fitness pass the same as the total cost without the fitness pass?
Let the number of classes be c.
For the fitness pass plan, we have the total cost of:
13c + 100
For the flat rate plan, we have the total cost of:
18c
The question asks for c when both plans are equal. So we set both costs equal and solve for c:
13c + 100 = 18c
We [URL='https://www.mathcelebrity.com/1unk.php?num=13c%2B100%3D18c&pl=Solve']type this equation into our math engine[/URL] and we get:
c = [B]20[/B]

Ordering Numbers

Given a list of numbers, this will order the list ascending (lowest to highest or least to greatest) or descending (highest to lowest or greatest to least)

Ordinal Number

This calculator determines the ordinal number of an integer

Oscar makes a large purchase at Home Depot and plans to rent one of its trucks to take his supplies

Oscar makes a large purchase at Home Depot and plans to rent one of its trucks to take his supplies home. The most he wants to spend on the truck is $56.00. If Home Depot charges $17.00 for the first 75 minutes and $5.00 for each additional 15 min, for how long can Oscar keep the truck and remain within his budget?
Set up the cost equation C(m) where m is the number of minutes for rental:
C(m) = 17 * min(m, 75) + max(0, 5(m - 75))
If Oscar uses the first 75 minutes, he spends $17. So he's left with:
$56 - $17 = $38
$38 / $5 = 7 Remainder 3
We remove the remainder 3, since it's not a full 15 minute block. So Oscar can rent the truck for:
7 * 15 minute blocks = [B]105 minutes[/B]

our recipe calls for 2 eggs and 3 cups of sugar. if we want to use 5 eggs, how much sugar will we ne

Our recipe calls for 2 eggs and 3 cups of sugar. if we want to use 5 eggs, how much sugar will we need?
Set up a relational proportion for eggs to cups of sugar where s is the number of cups of sugar we need for 5 eggs.
2/3 = 5/s
[URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=5&den1=3&den2=s&propsign=%3D&pl=Calculate+missing+proportion+value']Plugging this into the search engine[/URL], we get [B]7.5 cups of sugar[/B].

Out of the 485 Cookies for the bake sale, 2/5 were chocolate chip. Estimate the number of chocolate

Out of the 485 Cookies for the bake sale, 2/5 were chocolate chip. Estimate the number of chocolate chips
We want 2/5 of 485. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=485&frac2=2/5&pl=Multiply']type this in our search engine[/URL] and we get;
[B]194[/B]

P is the natural numbers that are factors of 25

P is the natural numbers that are factors of 25
we type in [I][URL='https://www.mathcelebrity.com/factoriz.php?num=25&pl=Show+Factorization']factor 25[/URL][/I] into our math engine and we get:
{1, 5, 25}
Since [U]all[/U] of these are natural numbers, our answer is:
[B]{1, 5, 25}[/B]

p(t)=6t represent the number of people p(t) that a number of turkeys can feed at Thanksgiving. How m

p(t)=6t represent the number of people p(t) that a number of turkeys can feed at Thanksgiving. How many people can 6 turkeys feed?
Plug in t = 6
p(6) = 6(6)
p(6) = 36

p(x)=2x-5 find the domain

p(x)=2x-5 find the domain
Using our[URL='http://www.mathcelebrity.com/function-calculator.php?num=2x-5&pl=Calculate'] function calculator[/URL]:
[B]All real numbers[/B]

Paper sells for 21 cents per pad. What will 5 pads cost?

Total Cost = Cost Per Pad * Number of Pads
Total Cost = 0.21 * 5
Total Cost = [B]$1.05[/B]

Partial Quotient

Divides 2 numbers using the Partial Quotient

Partial Sum

Calculates a partial sum for 2 numbers.

Paul can walk 15 steps in 5 minutes How long does it take Paul to walk 75 steps at the same speed

Paul can walk 15 steps in 5 minutes How long does it take Paul to walk 75 steps at the same speed
Set up a proportion of steps to minutes where m is the number of minutes to walk 75 steps:
15/5 = 75/m
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=75&den1=5&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
m = [B]25[/B]

Penny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% each

Penny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% each year since. Let x = the number of years since 2010 and y = the value of the car. What will the value of the car be in 2020? Write the equation, using the variables above, that represents this situation and solve the problem, showing the calculation you did to get your solution. Round your answer to the nearest whole number.
We have the equation y(x):
y(x) = 25,000(0.97)^x <-- Since a 3 % decrease is the same as multiplying the starting value by 0.97
The problem asks for y(2020). So x = 2020 - 2010 = 10.
y(10) = 25,000(0.97)^10
y(10) = 25,000(0.73742412689)
y(10) = [B]18,435.60[/B]

Pentagonal Number

This calculator determines the nth pentagonal number

Percent Math

Simplifies expressions involving numbers and percents with respect to addition and subtraction

Percentage-Decimal-Fraction Relations

Calculates the relational items between a fraction, a decimal (including repeating decimal and terminating decimal), a percentage, and the numerator and denominator piece of that fraction. Also calculates the percentage change going from one number to another or the amount increase or decrease of a percentage above/below a number. Round decimals. decimals into fractions

Permutations and Combinations

Calculates the following:

Number of permutation(s) of n items arranged in r ways =_{n}P_{r}

Number of combination(s) of n items arranged in r__unique__ ways = _{n}C_{r} including subsets of sets

Number of permutation(s) of n items arranged in r ways =

Number of combination(s) of n items arranged in r

Pet supplies makes a profit of $5.50 per bag, if the store wants to make a profit of no less than $5

Pet supplies makes a profit of $5.50 per bag, if the store wants to make a profit of no less than $5225, how many bags does it need to sell?
5.5ob >= $5,225
Divide each side of the inequality by $5.50
b >=9.5 bags, so round up to a whole number of 10 bags.

Peter has $500 in his savings account. He purchased an iPhone that charged him $75 for his activatio

Peter has $500 in his savings account. He purchased an iPhone that charged him $75 for his activation fee and $40 per month to use the service on the phone. Write an equation that models the number of months he can afford this phone.
Let m be the number of months. Our equation is:
[B]40m + 75 = 500 [/B] <-- This is the equation
[URL='https://www.mathcelebrity.com/1unk.php?num=40m%2B75%3D500&pl=Solve']Type this equation into the search engine[/URL], and we get:
m = [B]10.625[/B]
Since it's complete months, it would be 10 months.

Peter was thinking of a number. Peter doubles it and adds 0.8 to get an answer of 31. Form an equati

Peter was thinking of a number. Peter doubles it and adds 0.8 to get an answer of 31. Form an equation with x from the information.
Take this algebraic expression in parts, starting with the unknown number x:
[LIST]
[*]x
[*][I]Double it [/I]means we multiply x by 2: 2x
[*]Add 0.8: 2x + 0.8
[*]The phrase [I]to get an answer of[/I] means an equation. So we set 2x + 0.8 equal to 31
[/LIST]
Build our final algebraic expression:
[B]2x + 0.8 = 31[/B]
[B][/B]
If you have to solve for x, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B0.8%3D31&pl=Solve']type this equation into our search engine[/URL] and we get:
x = 15.1

Peter’s Lawn Mowing Service charges $10 per job and $0.20 per square yard. Peter earns $25 for a job

Peter’s Lawn Mowing Service charges $10 per job and $0.20 per square yard. Peter earns $25 for a job.
Let y be the number of square yards. We have the following equation:
0.2y + 10 = 25
To solve for y, we[URL='https://www.mathcelebrity.com/1unk.php?num=0.2y%2B10%3D25&pl=Solve'] type this equation into our search engine [/URL]and we get:
y = [B]75[/B]

Phone Number Translator

Given a phone number with letters in it, this calculator will determine the numeric phone number for you to dial.

Place Value

Given a whole number or a decimal, the calculator will perform place number analysis on each place in your number.

For the whole and decimal portion, the calculator goes out to the 100 trillion mark.

For the whole and decimal portion, the calculator goes out to the 100 trillion mark.

please answer this word problem

Time 1, distance apart is 105 + 85 = 190
So every hour, the distance between them is 190 * t where t is the number of hours. Set up our distance function:
D(t) = 190t
We want D(t) = 494
190t = 494
Divide each side by 190
[B]t = 2.6 hours[/B]

please solve the fifth word problem

Find what was used:
Used Money = Prepaid original cost - Remaining Credit
Used Money = 20 - 17.47
Used Money = 2.53
Using (m) as the number of minutes, we have the following cost equation:
C(m) = 0.11m
C(m) = 2.53, so we have:
0.11m = 2.53
Divide each side by 0.11
[B]m = 23[/B]

please solve the fourth word problem

The sum of three numbers is
105
. The first number is
5
less than the second. The third number is
3
times the second. What are the numbers?

please solve the fourth word problem

Let x be the first number, y be the second number, and z be the number. We have the following equations:
[LIST=1]
[*]x + y + z = 305
[*]x = y - 5
[*]z = 3y
[/LIST]
Substitute (2) and (3) into (1)
(y - 5) + y + (3y) = 305
Combine like terms:
5y - 5 = 305
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=5y-5%3D305&pl=Solve']equation solver[/URL]
[B]y = 62
[/B]
Substitute y = 62 into (3)
z = 3(62)
[B]z = 186
[/B]
x = (62) - 5
[B]x = 57[/B]

Point P is located at -15 and point Q is located at 6 on a number line. Which value would represent

Point P is located at -15 and point Q is located at 6 on a number line. Which value would represent point T, the midpoint of PQ?
Using our [URL='https://www.mathcelebrity.com/mptnline.php?ept1=-15&empt=&ept2=6&pl=Calculate+missing+Number+Line+item']midpoint calculator[/URL], we get:
T = [B]-4.5[/B]

Poisson Distribution

Calculates the probability of 3 separate events that follow a poisson distribution.

It calculates the probability of exactly k successes P(x = k)

No more than k successes P (x <= k)

Greater than k successes P(x >= k)

Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

It calculates the probability of exactly k successes P(x = k)

No more than k successes P (x <= k)

Greater than k successes P(x >= k)

Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.

Calculates moment number t using the moment generating function

Polygons

Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon.
This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.

porportion problems

Set up a proportion of miles to minutes where m is the number of miles walked in 110 minutes:
5/60 = m/110
Use our [URL='http://www.mathcelebrity.com/prop.php?num1=5&num2=m&den1=60&den2=110&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
[B]m = 9.1667 miles[/B]

positive even numbers less than 10

positive even numbers less than 10
First, list out all positive even numbers less than 10.
Less than 10 means we do [U]not[/U] include 10.
[B]{2, 4, 6, 8}
[MEDIA=youtube]5YsPQo_2dpI[/MEDIA][/B]

Positive numbers less than 4

Update, this has been added to our shortcuts.
You can type any expression in the form, positive numbers less than x where x is any integer.
You can also type positive numbers greater than x where x is any integer.
Same with less than or equal to and greater than or equal to.

Powers Of

Determines the powers of a number from 1 to n.

Predecessor

Calculates the predecessor number to a given number

Prime Numbers

Shows up to 3000 prime numbers and a cumulative sum

Primitive Root

Given a prime number p and a potential root of b, this determines if b is a primitive root of p.

Prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and tw

Imagine you are in a game show. Prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and two are worth $10. You have to pay $20 to the host if your choice is not correct. Let the random variable x be the winning
(a) What is your expected winning in this game?
(b) Determine the standard deviation of x. (Round the answer to two decimal places)
(a) 100(0.1) + 50(0.1) + 10(0.2) - 20 = 10 + 5 + 2 - 20 = [B]-3[/B]
(b) 3.3 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=+100,50,10&num2=+0.1,0.1,0.2&usep=usep&pl=Number+Set+Basics']standard deviation calculator[/URL]

product of a number and its reciprocal is increased by 7

product of a number and its reciprocal is increased by 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Its reciprocal means we take the reciprocal of x:
1/x
product of a number and its reciprocal:
x * 1/x
x/x
The x's cancel giving us:
1
is increased by 7 means we add 7:
1 + 7
[B]8[/B]

Product of Consecutive Numbers

Finds the product of (n) consecutive integers, even or odd as well. Examples include:

product of 2 consecutive integers

product of 2 consecutive numbers

product of 2 consecutive even integers

product of 2 consecutive odd integers

product of 2 consecutive even numbers

product of 2 consecutive odd numbers

product of two consecutive integers

product of two consecutive odd integers

product of two consecutive even integers

product of two consecutive numbers

product of two consecutive odd numbers

product of two consecutive even numbers

product of 3 consecutive integers

product of 3 consecutive numbers

product of 3 consecutive even integers

product of 3 consecutive odd integers

product of 3 consecutive even numbers

product of 3 consecutive odd numbers

product of three consecutive integers

product of three consecutive odd integers

product of three consecutive even integers

product of three consecutive numbers

product of three consecutive odd numbers

product of three consecutive even numbers

product of 4 consecutive integers

product of 4 consecutive numbers

product of 4 consecutive even integers

product of 4 consecutive odd integers

product of 4 consecutive even numbers

product of 4 consecutive odd numbers

product of four consecutive integers

product of four consecutive odd integers

product of four consecutive even integers

product of four consecutive numbers

product of four consecutive odd numbers

product of four consecutive even numbers

product of 5 consecutive integers

product of 5 consecutive numbers

product of 5 consecutive even integers

product of 5 consecutive odd integers

product of 5 consecutive even numbers

product of 5 consecutive odd numbers

product of five consecutive integers

product of five consecutive odd integers

product of five consecutive even integers

product of five consecutive numbers

product of five consecutive odd numbers

product of five consecutive even numbers

product of 2 consecutive integers

product of 2 consecutive numbers

product of 2 consecutive even integers

product of 2 consecutive odd integers

product of 2 consecutive even numbers

product of 2 consecutive odd numbers

product of two consecutive integers

product of two consecutive odd integers

product of two consecutive even integers

product of two consecutive numbers

product of two consecutive odd numbers

product of two consecutive even numbers

product of 3 consecutive integers

product of 3 consecutive numbers

product of 3 consecutive even integers

product of 3 consecutive odd integers

product of 3 consecutive even numbers

product of 3 consecutive odd numbers

product of three consecutive integers

product of three consecutive odd integers

product of three consecutive even integers

product of three consecutive numbers

product of three consecutive odd numbers

product of three consecutive even numbers

product of 4 consecutive integers

product of 4 consecutive numbers

product of 4 consecutive even integers

product of 4 consecutive odd integers

product of 4 consecutive even numbers

product of 4 consecutive odd numbers

product of four consecutive integers

product of four consecutive odd integers

product of four consecutive even integers

product of four consecutive numbers

product of four consecutive odd numbers

product of four consecutive even numbers

product of 5 consecutive integers

product of 5 consecutive numbers

product of 5 consecutive even integers

product of 5 consecutive odd integers

product of 5 consecutive even numbers

product of 5 consecutive odd numbers

product of five consecutive integers

product of five consecutive odd integers

product of five consecutive even integers

product of five consecutive numbers

product of five consecutive odd numbers

product of five consecutive even numbers

Prove 0! = 1

Prove 0! = 1
Let n be a whole number, where n! represents the product of n and all integers below it through 1.
The factorial formula for n is:
n! = n · (n - 1) * (n - 2) * ... * 3 * 2 * 1
Written in partially expanded form, n! is:
n! = n * (n - 1)!
[U]Substitute n = 1 into this expression:[/U]
n! = n * (n - 1)!
1! = 1 * (1 - 1)!
1! = 1 * (0)!
For the expression to be true, 0! [U]must[/U] equal 1. Otherwise, 1! <> 1 which contradicts the equation above

Prove sqrt(2) is irrational

Use proof by contradiction. Assume sqrt(2) is rational.
This means that sqrt(2) = p/q for some integers p and q, with q <>0.
We assume p and q are in lowest terms.
Square both side and we get:
2 = p^2/q^2
p^2 = 2q^2
This means p^2 must be an even number which means p is also even since the square of an odd number is odd.
So we have p = 2k for some integer k. From this, it follows that:
2q^2 = p^2 = (2k)^2 = 4k^2
2q^2 = 4k^2
q^2 = 2k^2
q^2 is also even, therefore q must be even.
So both p and q are even.
This contradicts are assumption that p and q were in lowest terms.
So sqrt(2) [B]cannot be rational.
[MEDIA=youtube]tXoo9-8Ewq8[/MEDIA][/B]

Put the number 123456789 exactly ones in the bubble so that each edge adds up to say number

Put the number 123456789 exactly ones in the bubble so that each edge adds up to say number
[B]
Each side adds up to 17
[IMG]https://www.mathcelebrity.com/images/triangle_sum_17.png[/IMG]
[/B]

Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?

Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?
From segment addition, we know that:
PQ + QR = PR
Plugging our given numbers in, we get:
2.7 + QR = 6.1
Subtract 2.7 from each side, and we get:
2.7 - 2.7 + QR = 6.1 - 2.7
Cancelling the 2.7 on the left side, we get:
QR = [B]3.4[/B]

quotient of the sum of 2 numbers and 6

quotient of the sum of 2 numbers and 6
The phrase [I]two numbers[/I] means we choose 2 arbitrary variables, let's call them x and y
x, y
The sum of 2 numbers:
x + y
quotient of the sum of 2 numbers and 6
[B](x + y)/6[/B]

Rachel buys some scarves that cost $10 each and 2 purses that cost $16 each. The cost of Rachel's to

Rachel buys some scarves that cost $10 each and 2 purses that cost $16 each. The cost of Rachel's total purchase is $62. What equation can be used to find n, the number of scarves that Rebecca buys
Scarves Cost + Purses Cost = Total Cost
[U]Calculate Scarves Cost[/U]
Scarves cost = Cost per scarf * number of scarves
Scarves cost = 10n
[U]Calculate Purses Cost[/U]
Purses cost = Cost per purse * number of purses
Purses cost = 16 * 2
Purses cost = 32
Total Cost = 62. Plug in our numbers and values to the Total Cost equation :
10n + 32 = 62
Solve for [I]n[/I] in the equation 10n + 32 = 62
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 32 and 62. To do that, we subtract 32 from both sides
10n + 32 - 32 = 62 - 32
[SIZE=5][B]Step 2: Cancel 32 on the left side:[/B][/SIZE]
10n = 30
[SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE]
10n/10 = 30/10
n = [B]3[/B]

Rachel saved $200 and spends $25 each week. Roy just started saving $15 per week. At what week will

Rachel saved $200 and spends $25 each week. Roy just started saving $15 per week. At what week will they have the same amount?
Let Rachel's account value R(w) where w is the number of weeks be:
R(w) = 200 - 25w <-- We subtract -25w because she spends it every week, decreasing her balance.
Let Roy's account value R(w) where w is the number of weeks be:
R(w) = 15w
Set them equal to each other:
200 - 25w = 15w
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=200-25w%3D15w&pl=Solve']we type it into our search engine[/URL] and get:
[B]w = 5[/B]

Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wedne

Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she sold 6 fewer books than she did on Tuesday. During the 3 days Rachel sold 19 books. Create an equation that can be used to find m, a number of books Rachel sold on Monday.
Let me be the number of books Rachel sold on Monday. We're given Tuesday's book sales (t) and Wednesday's books sales (w) as:
[LIST=1]
[*]t = 2m
[*]w = t - 6
[*]m + t + w = 19
[/LIST]
Plug (1) and (2) into (3):
Since t = 2m and w = t - 6 --> 2m - 6, we have:
m + 2m + 2m - 6 = 19
Combine like terms:
5m - 6 = 19
[URL='https://www.mathcelebrity.com/1unk.php?num=5m-6%3D19&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]m = 5[/B]

Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every c

Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every copy of Math is Fun he sells. Let p represent his total pay (in dollars), and let c represent the number of copies of Math is Fun he sells. Write an equation relating to . Then use this equation to find his total pay if he sells 22 copies of Math is Fun.
We want a sales function p where c is the number of copies of Math is Fun
p = Price per sale * c + Base Salary
[B]p = 40c + 1900
[/B]
Now, we want to know Total pay if c = 22
p = 40(22) + 1900
p = 880 + 1900
p = [B]2780[/B]

Random Number Generator

This program generates (n) random numbers between a set of values you specify.

Example: Generate 5 random numbers between 0 and 100.

Example: Generate 5 random numbers between 0 and 100.

Ratio Word Problems

Solves a ratio word problem using a given ratio of 2 items in proportion to a whole number.

Rational Number Subtraction

Subtracting 2 numbers, this shows an equivalent operations is adding the additive inverse. p - q = p + (-q)

Rational Numbers

This lesson walks you through what rational numbers are, how to write rational numbers, rational number notation, and what's included in rational numbers

Rational Numbers Between

This calculator determines all rational numbers between two numbers

Rational,Irrational,Natural,Integer Property

This calculator takes a number, decimal, or square root, and checks to see if it has any of the following properties:

* Integer Numbers

* Natural Numbers

* Rational Numbers

* Irrational Numbers Handles questions like: Irrational or rational numbers Rational or irrational numbers rational and irrational numbers Rational number test Irrational number test Integer Test Natural Number Test

* Integer Numbers

* Natural Numbers

* Rational Numbers

* Irrational Numbers Handles questions like: Irrational or rational numbers Rational or irrational numbers rational and irrational numbers Rational number test Irrational number test Integer Test Natural Number Test

Reagan bought t T-shirts. The shirts came in 8 packages. Write an expression that shows how many T-s

Reagan bought t T-shirts. The shirts came in 8 packages. Write an expression that shows how many T-shirts were in each package.
T-shirts per package = number of packages / number of t-shirts per package
T-shirts per package = [B]8/t[/B]

Real Numbers

This lesson walks you through what real numbers are, how to write real numbers, real numbers notation, and what's included in real numbers

Rectangular Number

This calculator determines the nth rectangular number

Reece made a deposite into an account that earns 8% simple interest. After 8 years reece has earned

Reece made a deposite into an account that earns 8% simple interest. After 8 years Reece has earned 400 dollars. How much was Reece's initial deposit?
Simple interest formula:
A = P(1 + it) where P is the amount of principal to be invested, i is the interest rate, t is the time, and A is the amount accumulated with interest.
Plugging in our numbers, we get:
400 = P(1 + 0.08(8))
400 = P(1 + 0.64)
400 = 1.64P
1.64P = 400
[URL='https://www.mathcelebrity.com/1unk.php?num=1.64p%3D400&pl=Solve']Typing this problem into our search engine[/URL], we get:
P = [B]$243.90[/B]

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a ball at random.
a. What is the probability that you choose a red or even numbered ball?
b. What is the probability you choose a green ball or a ball numbered less than 5?
a. The phrase [I]or[/I] in probability means add. But we need to subtract even reds so we don't double count:
We have 18 total balls, so this is our denonminator for our fractions.
Red and Even balls are {2, 4, 6, 8, 10, 12}
Our probability is:
P(Red or Even) = P(Red) + P(Even) - P(Red and Even)
P(Red or Even) = 13/18 + 9/18 - 6/18
P(Red or Even) = 16/18
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=16%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have:
P(Red or Even) = [B]16/18[/B]
[B][/B]
b. The phrase [I]or[/I] in probability means add. But we need to subtract greens less than 5 so we don't double count:
We have 18 total balls, so this is our denonminator for our fractions.
Green and less than 5 does not exist, so we have no intersection
Our probability is:
P(Green or Less Than 5) = P(Green) + P(Less Than 5) - P(Green And Less Than 5)
P(Green or Less Than 5) = 5/18 + 4/18 - 0
P(Green or Less Than 5) = 9/18
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have:
P(Red or Even) = [B]1/2[/B]

Reflexive Property

Demonstrates the reflexive property of congruence using a number.
Numerical Properties

Regrouping

Subtracts two numbers using regrouping

Renee sells 6 gifts in 20 minutes. How many might she sell in 4 hrs

Renee sells 6 gifts in 20 minutes. How many might she sell in 4 hrs
What is 4 hours in minutes?
4 hours = 4 * 60 = 240 minutes.
Now we are on a minutes to minutes basis, set up a proportion:
6/20 = x/240 where x is the number of gifts in 240 minutes (4 hours)
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=6&num2=x&den1=20&den2=240&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
[B]x = 72[/B]

Represent the number of inches in 7 feet

Represent the number of inches in 7 feet
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=7&pl=Calculate&type=foot']type in 7 feet to our search engine and we get[/URL]:
7 feet = [B]84 inches[/B]

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacie

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate if 0.06 m per day.
Which function can be used to find the thickness of the ice shelf in meters x days since the discovery?
We want to build an function I(x) where x is the number of days since the ice shelf discovery.
We start with 450 meters, and each day (x), the ice shelf loses 0.06m, which means we subtract this from 450.
[B]I(x) = 450 - 0.06x[/B]

Rick sold a total of 75 books during the first 22 days of May. If he continues to sell books at the

Rick sold a total of 75 books during the first 22 days of May. If he continues to sell books at the same rate, how many books will he sell during the month of May?
Set up a proportion of days to books where n is the number of books sold in May:
22/31 = 75/n
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=22&num2=75&den1=31&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] and rounding to the next integer, we get:
n = [B]106[/B]

Ricky reads 20 pages in 50 minutes. How many minutes does it take him to read one page

Ricky reads 20 pages in 50 minutes. How many minutes does it take him to read one page
Set up a proportion of pages per minute where m is the number of minutes to read one page:
20/50 = 1/m
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=20&num2=1&den1=50&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
m = [B]2.5[/B]

Riley is trying to raise money by selling key chains. each key chain costs $2.50. If riley is trying

Riley is trying to raise money by selling key chains. each key chain costs $2.50. If riley is trying to raise $60. How many key chains will he have to sell
Let the number of key chains be k. We have the following equation:
2.50k = 60
To solve this equation for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.50k%3D60&pl=Solve']type it in our search engine[/URL] and we get:
k = [B]24[/B]

Rob has 40 coins, all dimes and quarters, worth $7.60. How many dimes and how many quarters does he

Rob has 40 coins, all dimes and quarters, worth $7.60. How many dimes and how many quarters does he have?
We have two equations where d is the number of dimes and q is the number of quarters:
[LIST=1]
[*]d + q = 40
[*]0.1d + 0.25q = 7.60
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=d+%2B+q+%3D+40&term2=0.1d+%2B+0.25q+%3D+7.60&pl=Cramers+Method']simultaneous equation calculator[/URL], we get:
[B]d = 16
q = 24[/B]

Robert has 45 dollars. He buys 6 tshirts and has 7 dollars left over. How much did each tshirt cost?

Let x be the price of one t-shirt. Set up an equation:
6 times the number of t-shirts plus 7 dollars left over get him to a total of 45
6x = 45 - 7
6x = 38
Divide each side by 6
[B]x = 6.33[/B]

Roberto has taken 17 photos photos are placed on each odd number page and the newspaper has 10 pages

Roberto has taken 17 photos photos are placed on each odd number page and the newspaper has 10 pages total. The pages with photographs will have 3 or 4 photos each. How many pages has 3 photos and how many pages have 4 photos?
Odd pages are 1, 3, 5, 7, 9
17/5 = 3 with 2 remaining.
So all 5 pages have 3 photos. Then with 2 left over, 2 pages get 4 photos.
So 5 pages have [B]3 photos, and 2 pages have 2 photos[/B]
3(3) + 4(2) = 9 + 8 = 17

Roberto owns a trucking company. He charges $50 hook up fee and $2 per mile. How much to tow your ca

Roberto owns a trucking company. He charges $50 hook up fee and $2 per mile. How much to tow your car: 1mile , 2miles , 10miles ?
The Cost Function C(m) where m is the number of miles is written as:
C(m) = 2m + 50
The problem asks for C(1), C(2), and C(10)
Calculate C(1)
C(1) = 2(1) + 50
C(1) = 2 + 50
C(1) = [B]52[/B]
Calculate C(2)
C(2) = 2(2) + 50
C(2) = 4 + 50
C(2) = [B]54[/B]
Calculate C(10)
C(10) = 2(10) + 50
C(10) = 20 + 50
C(10) = [B]70[/B]

Roman Numeral Conversions

Converts a Positive integer less than 4000 to a Roman Numeral.

Converts a Roman Numeral with a positive value less than 4000 to a number.

Converts a Roman Numeral with a positive value less than 4000 to a number.

Ronnie, liza, vivien, and vina are classmates. They send each other a Valentines card. Find the numb

Ronnie, liza, vivien, and vina are classmates. They send each other a Valentines card. Find the number of Valentines cards they send altogether
We've got 4 classmates. Which means each person sends 3 Valentine's cards (to everybody else in the class but themselves):
3 * 3 * 3 * 3 or 4 * 3 = 12 Valentine's cards.

Rose weighs 140 pounds and gains 10%. What percent of her new weight must she lose to get back to 14

Rose weighs 140 pounds and gains 10%. What percent of her new weight must she lose to get back to 140 pounds?
Find her new weight after the 10% gain:
New Weight = Starting Weight * (1 + 10%)
Since 10% is 0.1, we have:
New Weight = Starting Weight * (1 + 0.1)
New Weight = Starting Weight * (1.1)
Plug in our numbers:
New Weight = 140 * (1.1)
New Weight = 154
To get back to 140, Rose must lose 154 - 140 = 14 pounds.
As a percentage of her new weight, [URL='https://www.mathcelebrity.com/perc.php?num=14&den=154&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']we type 14/154 into our search engine[/URL], and get:
[B]9.09%
[/B]
[I]We read this as, Rose must lose 9.09% of her current body weight of 154 pounds to get back to her starting weight of 140 pounds.[/I]

Roster Notation

Given a set of numbers, this displays the roster notation

Roulette Cumulative Betting

This calculator displays the probability and return grid for a roulette scenario where you play x games, betting y per number playing z numbers per game.

Rounding

Rounds a number to the nearest number of your choice

Rounding to Decimal Places

Rounds a number to a select number of decimal places

s = tu^2 for u

s = tu^2 for u
Divide each side by t
u^2 = s/t
Take the square root of each side
[LIST]
[*]u = sqrt(s/t)
[*]u = -sqrt(s/t)
[/LIST]
We have two answers due to negative number squared is positive

Sally and Adam works a different job. Sally makes $5 per hour and Adam makes $4 per hour. They each

Sally and Adam works a different job. Sally makes $5 per hour and Adam makes $4 per hour. They each earn the same amount per week but Adam works 2 more hours. How many hours a week does Adam work?
[LIST]
[*]Let [I]s[/I] be the number of hours Sally works every week.
[*]Let [I]a[/I] be the number of hours Adam works every week.
[*]We are given: a = s + 2
[/LIST]
Sally's weekly earnings: 5s
Adam's weekly earnings: 4a
Since they both earn the same amount each week, we set Sally's earnings equal to Adam's earnings:
5s = 4a
But remember, we're given a = s + 2, so we substitute this into Adam's earnings:
5s = 4(s + 2)
Multiply through on the right side:
5s = 4s + 8 <-- [URL='https://www.mathcelebrity.com/expand.php?term1=4%28s%2B2%29&pl=Expand']multiplying 4(s + 2)[/URL]
[URL='https://www.mathcelebrity.com/1unk.php?num=5s%3D4s%2B8&pl=Solve']Typing this equation into the search engine[/URL], we get s = 8.
The problem asks for Adam's earnings (a). We plug s = 8 into Adam's weekly hours:
a = s + 2
a = 8 + 2
[B]a = 10[/B]

Sally found 73 seashells on the beach, she gave Mary some of her seashells. She has 10 left. How man

Sally found 73 seashells on the beach, she gave Mary some of her seashells. She has 10 left. How many did she give to Mary?
Let the number of seashells Sally gave away as g. We're given:
73 - g = 10
To solve this equation for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=73-g%3D10&pl=Solve']type it in our search engine[/URL] and we get:
g = [B]63[/B]

Sally worked for 35 hours and was paid 8 dollars per hour how much money did she earn

Sally worked for 35 hours and was paid 8 dollars per hour how much money did she earn?
Total Wages = Number of Hours Worked * Hourly Rate
Total Wages = 35 * 8
Total Wages = [B]280[/B]

Salma purchased a prepaid phone card for 30. Long distance calls cost 9 cents a minute using this ca

Salma purchased a prepaid phone card for 30. Long distance calls cost 9 cents a minute using this card. Salma used her card only once to make a long distance call. If the remaining credit on her card is 28.38, how many minutes did her call last?
[U]Set up the equation where m is the number of minutes used:[/U]
0.09m = 30 - 28.38
0.09m = 1.62
[U]Divide each side by 0.09[/U]
[B]m = 18[/B]

Sam can pick 56 apples in 30 minutes. How many can he pick in 45 minutes?

Sam can pick 56 apples in 30 minutes. How many can he pick in 45 minutes?
We set up a proportion of apples to minutes where a is the number of apples Sam can pick in 45 minutes.
56/30 = a/45
Using our math engine, we [URL='https://www.mathcelebrity.com/prop.php?num1=56&num2=a&den1=30&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search box[/URL] and get:
a = [B]84
[MEDIA=youtube]tpNHh1jh3XE[/MEDIA][/B]

Sam finished 18 problems in one hour. How many hours will it take same to solve 80 problems

Sam finished 18 problems in one hour. How many hours will it take same to solve 80 problems
Set up a proportion of problems to hours where h is the number of hours for 80 problems:
18/1 = 80/h
To solve for h, we [URL='https://www.mathcelebrity.com/prop.php?num1=18&num2=80&den1=1&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search engine [/URL]and we get:
h = [B]4.44[/B]

Sam has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how

Sam has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how many dimes?
Let d be the number of dimes. Let q be the number of quarters. We're given two equations:
[LIST=1]
[*]0.1d + 0.25q = 2.25
[*]d + q = 12
[/LIST]
We have a simultaneous system of equations. We can solve this 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]d = 5[/B]
[*][B]q = 7[/B]
[/LIST]

Sam is eating a Big Hamburger. The first bite was 20% of the Hamburger, the second bite was 20% of w

Sam is eating a Big Hamburger. The first bite was 20% of the Hamburger, the second bite was 20% of what is left and so every next bite is 20% of what is left. b Is it possible for Sam to eat it all if he will bite 20% of what it is left?
[B]No, this will go on for infinity.
[/B]
The number gets closer to 0 but never hits 0.

Sam needs to save $300 to buy a video game system. He is able to save $20 per week. How many weeks w

Sam needs to save $300 to buy a video game system. He is able to save $20 per week. How many weeks will it take till he can buy the video game system?
Let w be the number of weeks. We have the following equation:
20w = 300
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=20w%3D300&pl=Solve']equation solver[/URL], we get:
[B]w = 15[/B]

Sam's plumbing service charges a $50 diagnostic fee and then $20 per hour. How much money does he ea

Sam's plumbing service charges a $50 diagnostic fee and then $20 per hour. How much money does he earn, m, when he shows up to your house to do a job that takes h hours
[U]Set up the cost equation:[/U]
m = Hourly Rate * h + service charge
[U]Plugging in our numbers, we get:[/U]
[B]m = 20h + 50[/B]

Sara has a box of candies. In the box there are 8 pink candies, 7 purple candies and 5 blue candies.

Sara has a box of candies. In the box there are 8 pink candies, 7 purple candies and 5 blue candies. She takes one candy and records its color. She then puts it back in the box and draws another candy. What is the probability of taking out a pink candy followed by a blue candy?
[B][U]Calculate the total number of candies:[/U][/B]
Total candies = Pink + Purple + Blue
Total candies = 8 + 7 + 5
Total candies = 20
[B][U]Calculate the probability of drawing one pink candy:[/U][/B]
P(Pink) = 8/20
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Pink) = 2/5
[B][U]Calculate the probability of drawing one blue candy:[/U][/B]
P(Blue) = 5/20 <-- [I]20 options since Sara replaced her first draw[/I]
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Blue) = 1/4
The problem asks for the probability of a Pink followed by a Blue. Since each event is independent, we multiply:
P(Pink, Blue) = P(Pink) * P(Blue)
P(Pink, Blue) = 2/5 * 1/4
P(Pink, Blue) = 2/20
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Pink, Blue) = [B]1/10 or 10%[/B]

Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money fro

Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money from her account and still have money left?
Let w be the number of weeks. We have the following equation for the Balance after w weeks:
B(w) = 250 - 25w [I]we subtract for withdrawals[/I]
The ability to withdrawal money means have a positive or zero balance after withdrawal. So we set up the inequality below:
250 - 25w >= 0
To solve this inequality for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=250-25w%3E%3D0&pl=Solve']type it in our search engine[/URL] and we get:
w <= [B]10
So Sarah can withdrawal for up to 10 weeks[/B]

Sarah makes $9 per hour working at a daycare center and $12 per hour working at a restaurant. Next

Sarah makes $9 per hour working at a daycare center and $12 per hour working at a restaurant. Next week, Sarah is scheduled to work 8 hours at the daycare center. Which of the following inequalities represents the number of hours (h) that Sandra needs to work at the restaurant next week to earn at least $156 from these two jobs?
Set up Sarah's earnings function E(h) where h is the hours Sarah must work at the restaurant:
12h + 9(8) >= 156 <-- The phrase [I]at least[/I] means greater than or equal to, so we set this up as an inequality. Also, the daycare earnings are $9 per hour * 8 hours
Multiplying through and simplifying, we get:
12h + 72 >= 156
We [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B72%3E%3D156&pl=Solve']type this inequality into the search engine[/URL], and we get:
[B]h>=7[/B]

Sarah starts with $300 in her savings account. She babysits and earns $30 a week to add to her accou

Sarah starts with $300 in her savings account. She babysits and earns $30 a week to add to her account. Write a linear equation to model this situation? Enter your answer in y=mx b form with no spaces.
Let x be the number of hours Sarah baby sits. Then her account value y is:
y = [B]30x + 300[/B]

Savannah is a salesperson who sells computers at an electronics store. She makes a base pay of $90 e

Savannah is a salesperson who sells computers at an electronics store. She makes a base pay of $90 each day and is also paid a commission for each sale she makes. One day, Savannah sold 4 computers and was paid a total of $100. Write an equation for the function P(x), representing Savannah's total pay on a day on which she sells x computers.
If base pay is $90 per day, then the total commission Savannah made for selling 4 computers is:
Commission = Total Pay - Base Pay
Commission = 100 - 90
Commission = $10
Assuming the commission for each computer is equal, we need to find the commission per computer:
Commission per computer = Total Commission / Number of Computers Sold
Commission per computer = 10/4
Commission per computer = $2.50
Now, we build the Total pay function P(x):
Total Pay = Base Pay + Commission * Number of Computers sold
[B]P(x) = 90 + 2.5x[/B]

Scientific Notation

* Converts a number into scientific notation and determines order of magnitude

* converts scientific notation to a number (standard notation). Also handles scientific notation operations.

* converts scientific notation to a number (standard notation). Also handles scientific notation operations.

Serial numbers for a product are to be using 3 letters followed by 4 digits. The letters are to be t

Serial numbers for a product are to be using 3 letters followed by 4 digits. The letters are to be taken from the first 8 letters of the alphabet with no repeats. The digits are taken from numbers 0-9 with no repeats. How many serial numbers can be generated
The serial number is organized with letters (L) and digits (D) like this:
LLLDDDD
Here's how we get the serial number:
[LIST=1]
[*]The first letter can be any of 8 letters A-H
[*]The second letter can be any 7 of 8 letters A-H
[*]The third letter can be any 6 of 8 letters A-H
[*]The fourth digit can be any of 10 digits 0-9
[*]The fifth digit can be any 9 of 10 digits 0-9
[*]The sixth digit can be any 8 of 10 digits 0-9
[*]The seventh digit can be any 7 of 10 digits 0-9
[/LIST]
We multiply all possibilities:
8 * 7 * 6 * 10 * 9 * 8 * 7
[B]1,693,440[/B]

Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are t

Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are to be taken from the first 5 letters of the alphabet with repeats possible and the numbers are taken from the digits 0 through 9 with no repeats, how many serial numbers can be generated?
First 5 letters of the alphabet are {A, B, C, D, E}
The 4 letters can be chosen as possible:
5 * 5 * 5 * 5
The number are not repeatable, so the 4 numbers can be chosen as:
10 * 9 * 8 * 7 since we have one less choice with each pick
Grouping letters and numbers together, we have the following serial number combinations:
5 * 5 * 5 * 5 * 10 * 9 * 8 * 7 = [B]3,150,000[/B]

Set C is the set of two-digit even numbers greater than 72 that do not contain the digit 8.

Set C is the set of two-digit even numbers greater than 72 that do not contain the digit 8.
First, two-digit numbers mean anything less than 100. Let's, list out our two-digit even numbers greater than 72 but less than 100.
C = {74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98}
The problem asks for numbers that do not contain the digit 8. Let's remove those numbers from the list.
C = {74, 76, [S]78[/S], [S]80, 82, 84, 86, 88[/S], 90, 92, 94, 96, [S]98[/S]}
[B]C = {74, 76, 90, 92, 94, 96}[/B]

Set C is the set of two-digit even numbers less than 56 that are divisible by 5

[U]Two digit Numbers less than 56:[/U]
{10, 11, 12, ..., 55}
[U]Two Digit Even Numbers of that Set:[/U]
{10, 12, 14, ..., 54}
[U]Two Digit Even numbers Divisible by 5[/U]
[B]C = {10, 20, 30, 40, 50}[/B]
[I]Note: Even means you can divide it by 2 with no remainder. Divisible by 5 means the number ends in 5 or 0. Since it is even numbers only, end in 0.[/I]

Set D is the set of two-digit even numbers less than 67 that are divisible by 5

Set D is the set of two-digit even numbers less than 67 that are divisible by 5
two-digit numbers start at 10. Divisible by 5 means the last digit is either 0 or 5. But even numbers don't end in 5, so we take the two-digit numbers ending in 0:
D = {[B]10, 20, 30, 40, 50, 60}[/B]

Set Notation

Given two number sets A and B, this determines the following:

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J_{σ}(A,B)

* Dice's Coefficient

* If A is a subset of B

* If B is a subset of A

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J

* Dice's Coefficient

* If A is a subset of B

* If B is a subset of A

Set of 2 digit even numbers less than 40

Set of 2 digit even numbers less than 40
Knowns and givens:
[LIST]
[*]2 digit numbers start at 10
[*]Less than 40 means we do not include 40
[*]Even numbers are divisible by 2
[/LIST]
[B]{10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38}[/B]

Seth is constantly forgetting the combination to his lock. He has a lock with four dials. (Each ha 1

Seth is constantly forgetting the combination to his lock. He has a lock with four dials. (Each has 10 numbers 0-9). If Seth can try one lock combination per second, how many seconds will it take him to try every possible lock combination?
Start with 0001, 0002, all the way to 9999
[URL='https://www.mathcelebrity.com/inclusnumwp.php?num1=0&num2=9999&pl=Count']When you do this[/URL], you get 10,000 combinations. One per second = 10,000 seconds

Seven less than 1/4 of a number is 9.

Seven less than 1/4 of a number is 9.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
1/4 of a number means we multiply x by 1/4:
x/4
Seven less than this means we subtract 7 from x/4:
x/4 - 7
The word [I]is[/I] means an equation, so we set x/4 - 7 equal to 9:
[B]x/4 - 7 = 9[/B]

Seven subtracted from the product of 3 and a number is greater than or equal to -26

Seven subtracted from the product of 3 and a number is greater than or equal to -26
[LIST=1]
[*]A number means an arbitrary variable, let's call it x.
[*]The product of 3 and a number is written as 3x
[*]Seven subtracted from 3x is written as 3x - 7
[*]Finally, that entire expression is greater than or equal to -26: [B]3x - 7 >= - 26[/B]
[/LIST]

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself how many

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself how many plums did she have at first?
Let p be the number of plums Shalini started with. We have:
[LIST]
[*]0.4 given to her brother
[*]20% which is 0.2 given away to her sister
[*]What this means is she kept 1 - (0.4 + 0.2) = 1 - 0.6 = 0.4 for herself
[/LIST]
0.4p = 16
Divide each side by 0.4
[B]p = 40[/B]

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself. How man

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself. How many plums did she have first?
Let's convert everything to decimals. 20% = 0.2
So Shalini gave 0.4 + 0.2 = 0.6 of the plums away. Which means she has 1 = 0.6 = 0.4 or 40% left over.
40% represents 16 plums
So our equation is 0.4p = 16 where p is the number of plums to start with
Divide each side by 0.4
[B]p = 40[/B]

Shanice won 97 pieces of gum playing basketball at the county fair. At school she gave four to every

Shanice won 97 pieces of gum playing basketball at the county fair. At school she gave four to every student in her math class. She only has 5 remaining. How many students are in her class?
Let the number of students be s. We have a situation described by the following equation:
4s + 5 = 97 <-- We add 5 since it's left over to get to 97
[URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B5%3D97&pl=Solve']We type this equation into the search engine[/URL] and we get:
s = [B]23[/B]

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked bot

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked both jobs for a total of 30 hours, and a total of $690. How long did Giselle work as a carpenter and how long did she work as a blacksmith?
Assumptions:
[LIST]
[*]Let b be the number of hours Giselle worked as a blacksmith
[*]Let c be the number of hours Giselle worked as a carpenter
[/LIST]
Givens:
[LIST=1]
[*]b + c = 30
[*]25b + 20c = 690
[/LIST]
Rearrange equation (1) to solve for b by subtracting c from each side:
[LIST=1]
[*]b = 30 - c
[*]25b + 20c = 690
[/LIST]
Substitute equation (1) into equation (2) for b
25(30 - c) + 20c = 690
Multiply through:
750 - 25c + 20c = 690
To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=750-25c%2B20c%3D690&pl=Solve']type this equation into our search engine[/URL] and we get:
c = [B]12
[/B]
Now, we plug in c = 12 into modified equation (1) to solve for b:
b = 30 - 12
b = [B]18[/B]

Sheila loaded 21 trucks every 28 minutes. At this rate how long will it take to load 12 trucks

Sheila loaded 21 trucks every 28 minutes. At this rate how long will it take to load 12 trucks.
Let m be the number of minutes it takes Sheila to load 12 trucks. We set up a proportion of trucks to minutes:
21/28 = 12/m
[URL='https://www.mathcelebrity.com/prop.php?num1=21&num2=12&den1=28&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL],and we get:
m = [B]16[/B]

Sierra borrows $310 from her brother to buy a lawn mower. She will repay $85 to start, and then anot

Sierra borrows $310 from her brother to buy a lawn mower. She will repay $85 to start, and then another $25 per week. A. Write an equation that can be used to determine w, the number of weeks it will take for Sierra to repay the entire amount.
Let w be the number of weeks. We have the equation:
25w + 85 = 310
[URL='https://www.mathcelebrity.com/1unk.php?num=25w%2B85%3D310&pl=Solve']Type this equation into the search engine[/URL], and we get:
w = [B]9[/B]

Sieve of Eratosthenes

Using the Sieve of Eratosthenes algorithm, this will show how many prime numbers are less than a number (n).

Sign Test

This will determine whether to accept or reject a null hypothesis based on a number set, mean value, alternative hypothesis, and a significance level using the Sign Test.

Since pounds are smaller than tons, i need to ______ the number of pounds by _____

Since pounds are smaller than tons, i need to ______ the number of pounds by _____
[B]Divide[/B] the number of pounds by [B]2,000[/B]

Six friends went out to dinner. Each person ordered the same dinner, which costs $15.85. The friends

Six friends went out to dinner. Each person ordered the same dinner, which costs $15.85. The friends left a combined tip of $14. What was the total of the bill and tip?
When all six friends eat the same meal, we calculate the total meal bill before the tip:
Total meal bill = Cost per Meal * Number of Friends
Total meal bill = 15.85 * 6
Total meal bill = $95.10
Calculate the Total bill and Tip:
Total Bill and Tip = Total Meal Bill + Tip
Total Bill and Tip = $95.10 + $14
Total Bill and Tip = [B]$109.10[/B]

Six Less than the total of three times a number and negative eight

Six Less than the total of three times a number and negative eight.
Let's take this in pieces:
Three times a number = 3x
The total of this and negative eight means we subtract eight
3x - 8
Six Less than this total means we subtract 6
3x - 8 - 6
Simplify by combining like terms:
[B]3x - 14[/B]

Six less than twice a number is at least -1 and at most 1

First, the phrase [I]a number[/I] means we choose an arbitrary variable, let's call it x.
Twice a number means we multiply it by 2.
2x
Six less than that means we subtract 6
2x - 6
Now, the last piece, we set up an inequality. At least -1 means greater than or equal to 1. At most 1 means less than or equal to 1. Notice, for both points, we include the number.
-1 <= 2x - 6 <= 1

slope is 0 and whose y-intercept is 9.

slope is 0 and whose y-intercept is 9.
The standard line equation is y = mx + b where m is the slope and b is the y-intercept is b.
Plugging in our numbers, we get:
y = 0x + 9
y = [B]9[/B]

Small pizzas were $3 and large pizzas were $5. To feed the throng, it was necessary to spend $475 fo

Small pizzas were $3 and large pizzas were $5. To feed the throng, it was necessary to spend $475 for 125 pizzas. How many small pizzas were purchased?
Let s be the number of small pizzas and l be the number of large pizzas. We have two given equations:
[LIST=1]
[*]l + s = 125
[*]3s + 5l = 475
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+s+%3D+125&term2=3s+%2B+5l+%3D+475&pl=Cramers+Method']simultaneous equation calculator[/URL], we get [B]s = 75[/B]:

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 c

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point.
Calculate the revenue function R(c) where s is the number of sodas sold:
R(s) = Sale Price * number of units sold
R(s) = 50s
Calculate the cost function C(s) where s is the number of sodas sold:
C(s) = Variable Cost * s + Fixed Cost
C(s) = 0.25s + 900
Our break-even point is found by setting R(s) = C(s):
0.25s + 900 = 50s
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]18.09[/B]

Solving word problems with the matrix method?

Hello everyone.
I am stuck on a work question that we are required to solve using the matrix (or Gauss-Jordan) method.
[CENTER]"A car rental company wants to buy 100 new cars. Compact cars cost $12,000 each,
intermediate size cars cost $18,000 each, full size cars cost $24,000 each, and the company
has a budget of $1,500,000. If they purchase twice as many compact cars as intermediate
sized cars, determine the number of cars of each type that they buy, assuming they
spend the entire budget."
[/CENTER]
I am fairly certain that I could solve this easily, except I cannot figure out the proper three equations that correspond to this question. I someone could help me figure them out, it would be greatly appreciated!

Some History teachers at Richmond High School are purchasing tickets for students and their adult ch

Some History teachers at Richmond High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Yang bought 30 student tickets and 30 adult tickets, which cost a total of $750. Mr. Alexander spent $682, getting 28 student tickets and 27 adult tickets. What is the price for each type of ticket?
Let the number of adult tickets be a
Let the number of student tickets be s
We're given two equations:
[LIST=1]
[*]30a + 30s = 750
[*]27a + 28s = 682
[/LIST]
To solve the simultaneous equations, we can use any of three methods below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we use, we get the same answers:
[LIST]
[*][B]a = 18[/B]
[*][B]s = 7[/B]
[/LIST]

Some scientists believe that there are 10^87 atoms in the entire universe. The number googolplex is

Some scientists believe that there are 10^87 atoms in the entire universe. The number googolplex is a 1 followed by a googol of zeros. If each atom in the universe is used as a zero, how many universes would you need in order to have enough zeros to write out completely the number googolplex?
10^100 zeros in the entire googolplex and 10^87 atoms in the universe
10^100 / 10^87 = [B]10^13 times as many zeros in the googolplex as there are atoms in the universe[/B]

Sports Pool Generator

This generator produces the following two sports (office) pools with shuffled scoring numbers (0 - 9):

1) Blank Sports Pool: This button generates a blank sports pool grid with shuffled numbers

2) Sports Pool with Names: This sports pool allows you to enter up to 100 names which will be randomly dropped into the blank grid boxes from Option 1 above.

This is easily copied and pasted into a program like Microsoft Word so that you can format it to your liking.

1) Blank Sports Pool: This button generates a blank sports pool grid with shuffled numbers

2) Sports Pool with Names: This sports pool allows you to enter up to 100 names which will be randomly dropped into the blank grid boxes from Option 1 above.

This is easily copied and pasted into a program like Microsoft Word so that you can format it to your liking.

Sports radio stations numbered 220 in 1996. The number of sports radio stations has since increased

Sports radio stations numbered 220 in 1996. The number of sports radio stations has since increased by approximately 14.3% per year. Write an equation for the number of sports radio stations for t years after 1996. If the trend continues, predict the number of sports radio stations in 2015.
Equation - where t is the number of years after 1996:
R(t) = 220(1.143)^t
We Want R(t) for 2015
t = 2015 - 1996 = 19
R(19) = 220(1.143)^19
R(19) = 220 * 12.672969
[B]R(19) = 2788.05 ~ 2,788[/B]

Square Number

This calculator determines the nth square number

Square Root Table

Generates a square root table for the first (n) numbers rounded to (r) digits

Square Roots and Exponents

Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following:

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x^{th} power denoted as n^{x} (Write without exponents)

* n raised to the x^{th} power raised to the yth power denoted as (n^{x})^{y} (Write without exponents)

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x

* n raised to the x

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

Squaring a number equals 5 times that number

Squaring a number equals 5 times that number.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Squaring this number:
x^2
5 times this number means we multiply by 5:
5x
The phrase [I]equals[/I] means we set both expressions equal to each other:
[B]x^2 = 5x [/B] <-- This is our algebraic expression
If you want to solve for x, then we subtract 5x from each side:
x^2 - 5x = 5x - 5x
Cancel the 5x on the right side, leaving us with 0:
x^2 - 5x = 0
Factor out x:
x(x - 5)
So we get x = 0 or [B]x = 5[/B]

Stanley earns $1160 a month. He spends $540 every month and saves the rest. How much will he save in

Stanley earns $1160 a month. He spends $540 every month and saves the rest. How much will he save in 4 years?
[U]Calculate savings amount per month:[/U]
Savings amount per month = Earnings - Spend
Savings amount per month = 1160 - 540
Savings amount per month = 620
[U]Convert years to months[/U]
4 years = 12 * 4 months
4 years = 48 months
[U]Calculate total savings:[/U]
Total Savings = Savings per month * number of months saved
Total Savings = 620 * 48
Total Savings = [B]$29,760
[MEDIA=youtube]sbzRra8dSFs[/MEDIA][/B]

Static Determinacy and Stability

Given a number of joints (j) and a number of members (m), this determines if a truss is statically determinate, statically indeterminate, or unstable

Stock A is worth 4.5. Stock B is worth 8.0. Stock C is worth 10.0. She purchased half as many shares

Stock A is worth 4.5. Stock B is worth 8.0. Stock C is worth 10.0. She purchased half as many shares of B as A and half as many shares of C as B. If her investments are worth 660, how many shares of each stock does she own?
Let s be the number of shares in Stock A. We have:
[LIST=1]
[*]A: 4.5s
[*]B: 8s/2 = 4s
[*]C: 10s/4 = 2.5s
[/LIST]
Value equation: 4.5s + 4s + 2.5s = 660
Combining like terms:
11s = 660
Using the [URL='http://www.mathcelebrity.com/1unk.php?num=11s%3D660&pl=Solve']equation calculator[/URL], we get [B]s = 60[/B] for Stock A
Stock B shares is equal to 1/2A = [B]30[/B]
Stock C shares is equal to 1/2B = [B]15[/B]

Students stuff envelopes for extra money. Their initial cost to obtain the information for the job w

Students stuff envelopes for extra money. Their initial cost to obtain the information for the job was $140. Each envelope costs $0.02 and they get paid $0.03per envelope stuffed. Let x represent the number of envelopes stuffed. (a) Express the cost C as a function of x. (b) Express the revenue R as a function of x. (c) Determine analytically the value of x for which revenue equals cost.
a) Cost Function
[B]C(x) = 140 + 0.02x[/B]
b) Revenue Function
[B]R(x) = 0.03x[/B]
c) Set R(x) = C(x)
140 + 0.02x = 0.03x
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=140%2B0.02x%3D0.03x&pl=Solve']equation solver[/URL], we get x = [B]14,000[/B]

subtract half of a number from 10

subtract half of a number from 10
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
half of a number means we divide x by 2:
x/2
subtract half of a number from 10
[B]10 - x/2[/B]

Successor

Calculates the successor number to a given number

sum of 3 consecutive odd integers equals 1 hundred 17

sum of 3 consecutive odd integers equals 1 hundred 17
The sum of 3 consecutive odd numbers equals 117. What are the 3 odd numbers?
1) Set up an equation where our [I]odd numbers[/I] are n, n + 2, n + 4
2) We increment by 2 for each number since we have [I]odd numbers[/I].
3) We set this sum of consecutive [I]odd numbers[/I] equal to 117
n + (n + 2) + (n + 4) = 117
[SIZE=5][B]Simplify this equation by grouping variables and constants together:[/B][/SIZE]
(n + n + n) + 2 + 4 = 117
3n + 6 = 117
[SIZE=5][B]Subtract 6 from each side to isolate 3n:[/B][/SIZE]
3n + 6 - 6 = 117 - 6
[SIZE=5][B]Cancel the 6 on the left side and we get:[/B][/SIZE]
3n + [S]6[/S] - [S]6[/S] = 117 - 6
3n = 111
[SIZE=5][B]Divide each side of the equation by 3 to isolate n:[/B][/SIZE]
3n/3 = 111/3
[SIZE=5][B]Cancel the 3 on the left side:[/B][/SIZE]
[S]3[/S]n/[S]3 [/S]= 111/3
n = 37
Call this n1, so we find our other 2 numbers
n2 = n1 + 2
n2 = 37 + 2
n2 = 39
n3 = n2 + 2
n3 = 39 + 2
n3 = 41
[SIZE=5][B]List out the 3 consecutive odd numbers[/B][/SIZE]
([B]37, 39, 41[/B])
37 ? 1st number, or the Smallest, Minimum, Least Value
39 ? 2nd number
41 ? 3rd or the Largest, Maximum, Highest Value

sum of a number and 7 is subtracted from 15 the result is 6.

Sum of a number and 7 is subtracted from 15 the result is 6.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take this expression in pieces. Sum of a number and 7
x + 7
Subtracted from 15
15 - (x + 7)
The result is means an equation, so we set this expression above equal to 6
[B]15 - (x + 7) = 6 <-- This is our algebraic expression[/B]
If the problem asks you to solve for x, we Group like terms
15 - x - 7 = 6
8 - x = 6
[URL='https://www.mathcelebrity.com/1unk.php?num=8-x%3D6&pl=Solve']Type 8 - x = 6 into the search engine[/URL], and we get [B]x = 2[/B]

Sum of a number and it's reciprocal is 6. What is the number?

Sum of a number and it's reciprocal is 6. What is the number?
Let the number be n.
The reciprocal is 1/n.
The word [I]is[/I] means an equation, so we set n + 1/n equal to 6
n + 1/n = 6
Multiply each side by n to remove the fraction:
n^2 + 1 = 6n
Subtract 6n from each side:
[B]n^2 - 6n + 1 = 0 [/B]<-- This is our algebraic expression
If the problem asks you to solve for n, then you [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-6n%2B1%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this quadratic equation into our search engine[/URL].

Sum of Consecutive Numbers

Finds the sum of (n) consecutive integers, even or odd as well. Examples include:

sum of 2 consecutive integers

sum of 2 consecutive numbers

sum of 2 consecutive even integers

sum of 2 consecutive odd integers

sum of 2 consecutive even numbers

sum of 2 consecutive odd numbers

sum of two consecutive integers

sum of two consecutive odd integers

sum of two consecutive even integers

sum of two consecutive numbers

sum of two consecutive odd numbers

sum of two consecutive even numbers

sum of 3 consecutive integers

sum of 3 consecutive numbers

sum of 3 consecutive even integers

sum of 3 consecutive odd integers

sum of 3 consecutive even numbers

sum of 3 consecutive odd numbers

sum of three consecutive integers

sum of three consecutive odd integers

sum of three consecutive even integers

sum of three consecutive numbers

sum of three consecutive odd numbers

sum of three consecutive even numbers

sum of 4 consecutive integers

sum of 4 consecutive numbers

sum of 4 consecutive even integers

sum of 4 consecutive odd integers

sum of 4 consecutive even numbers

sum of 4 consecutive odd numbers

sum of four consecutive integers

sum of four consecutive odd integers

sum of four consecutive even integers

sum of four consecutive numbers

sum of four consecutive odd numbers

sum of four consecutive even numbers

sum of 5 consecutive integers

sum of 5 consecutive numbers

sum of 5 consecutive even integers

sum of 5 consecutive odd integers

sum of 5 consecutive even numbers

sum of 5 consecutive odd numbers

sum of five consecutive integers

sum of five consecutive odd integers

sum of five consecutive even integers

sum of five consecutive numbers

sum of five consecutive odd numbers

sum of five consecutive even numbers

sum of 2 consecutive integers

sum of 2 consecutive numbers

sum of 2 consecutive even integers

sum of 2 consecutive odd integers

sum of 2 consecutive even numbers

sum of 2 consecutive odd numbers

sum of two consecutive integers

sum of two consecutive odd integers

sum of two consecutive even integers

sum of two consecutive numbers

sum of two consecutive odd numbers

sum of two consecutive even numbers

sum of 3 consecutive integers

sum of 3 consecutive numbers

sum of 3 consecutive even integers

sum of 3 consecutive odd integers

sum of 3 consecutive even numbers

sum of 3 consecutive odd numbers

sum of three consecutive integers

sum of three consecutive odd integers

sum of three consecutive even integers

sum of three consecutive numbers

sum of three consecutive odd numbers

sum of three consecutive even numbers

sum of 4 consecutive integers

sum of 4 consecutive numbers

sum of 4 consecutive even integers

sum of 4 consecutive odd integers

sum of 4 consecutive even numbers

sum of 4 consecutive odd numbers

sum of four consecutive integers

sum of four consecutive odd integers

sum of four consecutive even integers

sum of four consecutive numbers

sum of four consecutive odd numbers

sum of four consecutive even numbers

sum of 5 consecutive integers

sum of 5 consecutive numbers

sum of 5 consecutive even integers

sum of 5 consecutive odd integers

sum of 5 consecutive even numbers

sum of 5 consecutive odd numbers

sum of five consecutive integers

sum of five consecutive odd integers

sum of five consecutive even integers

sum of five consecutive numbers

sum of five consecutive odd numbers

sum of five consecutive even numbers

Sum of Five Consecutive Integers

Finds five consecutive integers, if applicable, who have a sum equal to a number.
Sum of 5 consecutive integers

Sum of Four Consecutive Integers

Finds four consecutive integers, if applicable, who have a sum equal to a number.
Sum of 4 consecutive integers

Sum of the First (n) Numbers

Determines the sum of the first (n)

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

Sum of Three Consecutive Integers

Finds three consecutive integers, if applicable, who have a sum equal to a number.
Sum of 3 consecutive integers

Sum of two consecutive numbers is always odd

Sum of two consecutive numbers is always odd
Definition:
[LIST]
[*]A number which can be written in the form of 2 m where m is an integer, is called an even integer.
[*]A number which can be written in the form of 2 m + 1 where m is an integer, is called an odd integer.
[/LIST]
Take two consecutive integers, one even, and one odd:
2n and 2n + 1
Now add them
2n + (2n+ 1) = 4n + 1 = 2(2 n) + 1
The sum is of the form 2n + 1 (2n is an integer because the product of two integers is an integer)
Therefore, the sum of two consecutive integers is an odd number.

SuperFit Gym charges $14 per month, as well as a one-time membership fee of $25 to join. After how m

SuperFit Gym charges $14 per month, as well as a one-time membership fee of $25 to join. After how many months will I spend a total of $165?
[U]Let the number of months be m. We have a total spend T of:[/U]
cost per month * m + one-time membership fee = T
[U]Plugging in our numbers, we get:[/U]
14m + 25 = 165
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=14m%2B25%3D165&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]10[/B]

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the populat

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the population of the city in 7 years
Set up the population function P(y) where y is the number of years since now:
P(y) = Current population + Growth per year * y
Plugging in our numbers at y = 7, we get:
P(7) = 740000 + 12620(7)
P(7) = 740000 + 88340
P(7) = [B]828,340[/B]

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the populat

Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the population of the city in 7 years.
We setup the population function P(y) where y is the number of years of population growth, g is the growth per year, and P(0) is the original population.
P(y) = P(0) + gy
Plugging in our numbers of y = 7, g = 12,620, and P(0) = 740,000, we have:
P(7) = 740,000 + 12,620 * 7
P(7) = 740,000 + 88,340
P(7) = [B]828,340[/B]

Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin doe

Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin does she have?
Set up two equations where d is the number of dimes and q is the number of quarters:
(1) d + q = 10
(2) 0.1d + 0.25q = 1.45
Rearrange (1) into (3) to solve for d
(3) d = 10 - q
Now plug (3) into (2)
0.1(10 - q) + 0.25q = 1.45
Multiply through:
1 - 0.1q + 0.25q = 1.45
Combine q terms
0.15q + 1 = 1.45
Subtract 1 from each side
0.15q = 0.45
Divide each side by 0.15
[B]q = 3[/B]
Plug our q = 3 value into (3)
d = 10 - 3
[B]d = 7[/B]

Suppose that J and K are on the number line. If JK=9 and J lies at 4 where could K be located?

Suppose that J and K are on the number line. If JK=9 and J lies at 4 where could K be located?
We'd need 9 spaces to the right of 4 or 9 spaces to the left of 4 to have JK be 9.
To the right:
K = 4 + 9
K = [B]13[/B]
K = 4 - 9
K = [B]-5[/B]

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in ga

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 20 gallons of fuel, the airplane weighs 2012 pounds. When carrying 55 gallons of fuel, it weighs 2208 pounds. How much does the airplane weigh if it is carrying 65 gallons of fuel?
Linear functions are written in the form of one dependent variable and one independent variable. Using g as the number of gallons and W(g) as the weight, we have:
W(g) = gx + c where c is a constant
We are given:
[LIST]
[*]W(20) = 2012
[*]W(55) = 2208
[/LIST]
We want to know W(65)
Using our givens, we have:
W(20) = 20x + c = 2012
W(55) = 55x + c = 2208
Rearranging both equations, we have:
c = 2012 - 20x
c = 2208 - 55x
Set them both equal to each other:
2012 - 20x = 2208 - 55x
Add 55x to each side:
35x + 2012 = 2208
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=35x%2B2012%3D2208&pl=Solve']equation solver[/URL], we see that x is 5.6
Plugging x = 5.6 back into the first equation, we get:
c = 2012 - 20(5.6)
c = 2012 - 112
c = 2900
Now that we have all our pieces, find W(65)
W(65) = 65(5.6) + 2900
W(65) = 264 + 2900
W(65) = [B]3264[/B]

Suppose we need 4 eggs to make a cake. If there are 24 eggs, write an inequality representing the po

Suppose we need 4 eggs to make a cake. If there are 24 eggs, write an inequality representing the possible number of cakes we can make.
Set up a proportion of eggs to cakes where c is the number of cakes per 24 eggs:
4/1 <= 24/c
[URL='https://www.mathcelebrity.com/prop.php?num1=4&num2=24&den1=1&den2=c&propsign=%3C&pl=Calculate+missing+proportion+value']Typing this proportion inequality into our search engine[/URL], we get:
[B]c <= 6[/B]

Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6.

Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6. When you divide x by 11 you get the same quotient but a remainder of 2. Find x.
[U]Use the quotient remainder theorem[/U]
A = B * Q + R where 0 ? R < B where R is the remainder when you divide A by B
Plugging in our numbers for Equation 1 we have:
[LIST]
[*]A = x
[*]B = 7
[*]Q = q
[*]R = 6
[*]x = 7 * q + 6
[/LIST]
Plugging in our numbers for Equation 2 we have:
[LIST]
[*]A = x
[*]B = 11
[*]Q = q
[*]R = 2
[*]x = 11 * q + 2
[/LIST]
Set both x values equal to each other:
7q + 6 = 11q + 2
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=7q%2B6%3D11q%2B2&pl=Solve']equation calculator[/URL], we get:
q = 1
Plug q = 1 into the first quotient remainder theorem equation, and we get:
x = 7(1) + 6
x = 7 + 6
[B]x = 13[/B]
Plug q = 1 into the second quotient remainder theorem equation, and we get:
x = 11(1) + 2
x = 11 + 2
[B]x = 13[/B]

Suppose you have $28.00 in your bank account and start saving $18.25 every week. Your friend has $16

Suppose you have $28.00 in your bank account and start saving $18.25 every week. Your friend has $161.00 in his account and is withdrawing $15 every week. When will your account balances be the same?
Set up savings and withdrawal equations where w is the number of weeks. B(w) is the current balance
[LIST]
[*]You --> B(w) = 18.25w + 28
[*]Your friend --> B(w) = 161 - 15w
[/LIST]
Set them equal to each other
18.25w + 28 = 161 - 15w
[URL='http://www.mathcelebrity.com/1unk.php?num=18.25w%2B28%3D161-15w&pl=Solve']Type that problem into the search engine[/URL], and you get [B]w = 4[/B].

Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on adverti

Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on advertising. You sell the book for $15 a copy. How many copies must you sell to break even.
Profit per book is:
P = 15 - 4
P = 11
We want to know the number of books (b) such that:
11b = 5500 <-- Breakeven means cost equals revenue
[URL='https://www.mathcelebrity.com/1unk.php?num=11b%3D5500&pl=Solve']Typing this equation into the search engine[/URL], we get:
b = [B]500[/B]

Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each.

Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each. This Saturday, she is renting a booth at a craft fair for $50. Write an equation that can be used to find the number of purses Susan must sell to make a profit of $295
Set up the cost function C(p) where p is the number of purses:
C(p) = Cost per purse * p + Booth Rental
C(p) = 15p + 50
Set up the revenue function R(p) where p is the number of purses:
R(p) = Sale price * p
R(p) = 30p
Set up the profit function which is R(p) - C(p) equal to 295
30p - (15p + 50) = 295
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=30p-%2815p%2B50%29%3D295&pl=Solve']we type it into our search engine[/URL] and we get:
p = [B]23[/B]

Susan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a c

Susan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a combined total of 104 hours at her two jobs. Let t be the number of hours Susan worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.
Let t be the number of hours for math tutoring and w be the number of hours for waitressing. We're given:
[LIST=1]
[*]t + w = 104
[*]14t + 13w = D <-- Combined total dollar amount
[/LIST]

Symmetric Property

Demonstrates the Symmetric property using a number.
Numerical Properties

T-Bill

Calculates any of the four items of the T-Bill (Treasury Bill or TBill) formula:

1) Price (P)

2) Face Value (F)

3) Number of Weeks (w)

4) Yield Rate (y)

1) Price (P)

2) Face Value (F)

3) Number of Weeks (w)

4) Yield Rate (y)

T-shirts sell for $19.97 and cost $14.02 to produce. Which equation represents p, the profit, in ter

T-shirts sell for $19.97 and cost $14.02 to produce. Which equation represents p, the profit, in terms of x, the number of t-shirts sold?
A) p = $19.97x - $14.02
B) p = x($19.97 - $14.02)
C) p = $19.97 + $14.02x
D) p = x($19.97 + $14.02)
[B]B) p = x($19.97 - $14.02)[/B]
[B][/B]
[LIST]
[*]Profit is Revenue - Cost
[*]Each shirt x generates a profit of 19.97 - 14.02
[/LIST]

Take a look at the following sums: 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 +

Take a look at the following sums:
1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
a. Come up with a conjecture about the sum when you add the first *n* odd numbers. For example, when you added the first 5 odd numbers (1 + 3 + 5 + 7 + 9), what did you get? What if wanted to add the first 10 odd numbers? Or 100?
b. Can you think of a geometric interpretation of this pattern? If you start with one square and add on three more, what can you make? If you now have 4 squares and add on 5 more, what can you make?
c. Is there a similar pattern for adding the first n even numbers?
2 = 2
2 + 4 = 6
2 + 4 + 6 = 12
2 + 4 + 6 + 8 = 20
a. The formula is [B]n^2[/B].
The sum of the first 10 odd numbers is [B]100[/B] seen on our s[URL='http://www.mathcelebrity.com/sumofthefirst.php?num=10&pl=Odd+Numbers']um of the first calculator[/URL]
The sum of the first 100 odd numbers is [B]10,000[/B] seen on our [URL='http://www.mathcelebrity.com/sumofthefirst.php?num=100&pl=Odd+Numbers']sum of the first calculator[/URL]
b. Geometric is 1, 4, 9 which is our [B]n^2[/B]
c. The sum of the first n even numbers is denoted as [B]n(n + 1)[/B] seen here for the [URL='http://www.mathcelebrity.com/sumofthefirst.php?num=+10&pl=Even+Numbers']first 10 numbers[/URL]

Ted tossed a number cube and rolled a die. How many possible outcomes are there?

Ted tossed a number cube and rolled a die. How many possible outcomes are there?
A number cube has 6 possible outcomes
A die has 6 possible outcomes.
We have 6 * 6 = [B]36 possible outcomes[/B].

Ten Frame

Builds a ten frame (dot card) for a number and shows numbers more and less.

Ten subtracted from the product of 9 and a number is less than ?24

Ten subtracted from the product of 9 and a number is less than ?24.
A number means an arbitrary variable, let's call it x
x
The product of 9 and a number:
9x
Ten subtracted from that
9x - 10
Finally, is less than means we set our entire expression less than -24
[B]9x - 10 < -24[/B]

Terry recorded the temperature every hour from 8 AM to 1 PM. The temperature at 8 AM was 19?. The te

Terry recorded the temperature every hour from 8 AM to 1 PM. The temperature at 8 AM was 19?. The temperature dropped 4? every hour. What was the temperature at 1 PM? Group of answer choices 1 degree
Set up our temperature function T(h) where h is the number of hours since 8 AM:
T(h) = 19 - 4h <-- We subtract 4h since each hour, the temperature drops 4 degrees
The questions asks for the temperature at 1PM. We need to figure out how many hours pass since 8 AM:
8 AM to 12 PM is 4 hours
12 PM to 1 PM is 1 hour
Total time is 5 hours
So we want T(5):
T(5) = 19 - 4(5)
T(5) = 19 - 20
T(5) = [B]-1?[/B]

The 4/7 part of a number is 84 . What is the number?

The 4/7 part of a number is 84 . What is the number?
We multiply 4/7 * 84.
7 goes into 84 12 times, so we have:
4 * 12 = [B]48[/B]

the absolute value of a number is its _____ from 0

the absolute value of a number is its _____ from 0
The answer is [B]distance[/B].
As an example: 2 and -2 are 2 units away from 0.

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 32

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 327 people entered the park , and the admission fee collected totaled 978.00 dollars . How many children and how many adults were admitted?
Let the number of children's tickets be c. Let the number of adult tickets be a. We're given two equations:
[LIST=1]
[*]a + c = 327
[*]4a + 1.50c = 978
[/LIST]
We can solve this system of equation 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answers:
[LIST]
[*][B]a = 195[/B]
[*][B]c = 132[/B]
[/LIST]

The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day,

The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day, 281 people entered the park, and the admission fees collected totaled $784 . How many children and how many adults were admitted?
Let c be the number of children and a be the number of adults. We have two equations:
[LIST=1]
[*]a + c = 281
[*]4a + 1.5c = 784
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a%2Bc%3D281&term2=4a+%2B+1.5c+%3D+784&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[LIST]
[*][B]a = 145[/B]
[*][B]c = 136[/B]
[/LIST]

The age of three sister are consecutive intergers the sum of their age is 45 what is their ages

The age of three sister are consecutive intergers the sum of their age is 45 what is their ages
Type this into the search engine: [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=thesumofthreeconsecutivenumbersis45&pl=Calculate']The sum of three consecutive numbers is 45[/URL].
We get [B]14, 15, 16[/B].

The ages of three siblings are all consecutive integers. The sum of of their ages is 39.

The ages of three siblings are all consecutive integers. The sum of of their ages is 39.
Let the age of the youngest sibling be n. This means the second sibling is n + 1. This means the oldest/third sibling is n + 2.
So what we want is the[URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof3consecutiveintegersequalto39&pl=Calculate'] sum of 3 consecutive integers equal to 39[/URL]. We type this command into our search engine. We get:
n = 12. So the youngest sibling is [B]12[/B].
The next sibling is 12 + 1 = [B]13[/B]
The oldest/third sibling is 12 + 2 = [B]14[/B]

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. Wha

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. What is the value of N ?
Average of the first number set is [URL='https://www.mathcelebrity.com/statbasic.php?num1=17%2C26%2C42%2C59&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']using our average calculator[/URL] is:
36
Now, the mean (average) or 19 and N is found by adding them together an dividing by 2:
(19 + N)/2
Since both number sets have equal means, we set (19 + N)/2 equal to 36:
(19 + N)/2 = 36
Cross multiply:
19 + N = 36 * 2
19 + n = 72
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=19%2Bn%3D72&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]53[/B]

The auditorium can hold a maximum of 150 people

The auditorium can hold a maximum of 150 people
We want an inequality for the number of people (p) in the auditorium.
The word [I]maximum[/I] means [I]no more than[/I] or [I]less than or equal to[/I]. So we have:
[B]p <= 150[/B]

The auto repair shop took 2.5 hours to repair Victoria’s car. The cost of parts was $93, and the tot

The auto repair shop took 2.5 hours to repair Victoria’s car. The cost of parts was $93, and the total bill was $248. What is the shops charge per hour.
Calculate Labor Cost:
Labor Cost = Total bill - Parts
Labor Cost = $248 - $93
Labor Cost = $155
Calculate labor hourly rate:
Labor Hourly Rate = Labor Cost / Number of Labor Hours
Labor Hourly Rate = 155/2.5
Labor Hourly Rate = [B]$62[/B]

The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the numbe

The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the number of books printed that day and k is a constant. Find k, if on the day when 200 were printed the average cost was $9 per book.
We are given: c(200) = 9, so we have:
9 = 5.5(200) + k(200)
200k + 1100 = 9
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=200k%2B1100%3D9&pl=Solve']equation solver[/URL], we get:
[B]k = -5.455[/B]

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height re

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother?
[LIST]
[*]Let the height of the family without the mom be f. Let the height of the mother be m.
[*]Averages mean we add the heights and divide by the number of people who were measured.
[/LIST]
We're given two equations:
[LIST=1]
[*](f + m)/6 = 6
[*]f/5 = 6
[/LIST]
Cross multiplying equation (2), we get:
f = 5 * 6
f = 30
Plug f = 30 into equation (1), we get:
(30 + m)/6 = 6
Cross multiplying, we get:
m + 30 = 6 * 6
m + 30 = 36
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B30%3D36&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]6[/B]
[SIZE=3][FONT=Arial][COLOR=rgb(34, 34, 34)][/COLOR][/FONT][/SIZE]

The average of 16 and x is 21. Find x.

The average of 16 and x is 21. Find x.
The average of 2 numbers is the sum of the 2 numbers divided by 2. So we have:
(16 + x)/2 = 21
Cross multiply:
16 + x = 21*2
16 + x = 42
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2Bx%3D42&pl=Solve']we type this expression into the search engine[/URL] and get [B]x = 26[/B].
Check our work by restating our answer:
The average of 16 and 26 is 21. TRUE.

The average of 171 and x?

The average of 171 and x?
The phrase [I]average[/I] means add up all the items in the number set, divided by the count of items in the number set.
Our number set in this case is {171, x} which has 2 elements. Therefore, our average is:
[B](171 + x)/2[/B]

The average of 20 numbers is 18 while the average of 18 numbers is 20. What is the average of the 38

The average of 20 numbers is 18 while the average of 18 numbers is 20. What is the average of the 38 numbers?
The average of averages is found by getting the sum of both groups of numbers and dividing by the count of numbers.
Calculate the sum of the first group of numbers S1:
Average = S1 / n1
18 = S1 / 20
S1 = 20 * 18
S1 =360
Calculate the sum of the second group of numbers S2:
Average = S2 / n2
20 = S2 / 18
S2 = 18 * 20
S2 =360
Our average of averages is found by the following:
A = (S1 + S2)/(n1 + n2)
A = (360 + 360)/(20 + 18)
A = 720/38
[B]A = 18.947[/B]

The average of a number and double the number is 25.5

Let x equal "a number".
Double the number is 2x.
The average is (x + 2x)/2
Combine the terms in the numerator:
3x/2
The word [I]is[/I] means equal to, so we set 3x/2 equal to 25.5
3x/2 = 25.5
Cross multiply the 2:
3x = 51
Divide each side by 3
[B]x = 17[/B]

the average of eighty-five and a number m is ninety

the average of eighty-five and a number m is ninety
Average of 2 numbers means we add both numbers and divide by 2:
(85 + m)/2 = 90
Cross multiply:
m + 85 = 90 * 2
m + 85 = 180
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B85%3D180&pl=Solve']type it in our math engine [/URL]and we get:
m = [B]95[/B]

the average of two numbers x and y

the average of two numbers x and y
Average is the sum divided by the count:
Sum:
x + y
We have 2 numbers, so we divide (x + y) by 2
[B](x + y)/2[/B]

The baseball coach bought 2 new baseballs for $1 each. The basketball coach bought 7 new basketballs

The baseball coach bought 2 new baseballs for $1 each. The basketball coach bought 7 new basketballs for $10 each. How much more did the basketball coach spend than the baseball coach?
[U]Baseball coach spend:[/U]
Spend = Number of baseballs * cost per baseball
Spend= 2 * $1
Spend = $2
[U]Basketball coach spend:[/U]
Spend = Number of basketballs * cost per basketball
Spend= 7 * $10
Spend = $70
[U]Calculate the difference in spend:[/U]
Difference = Basketball coach spend - Baseball coach spend
Difference= $70 - $2
Difference= [B]$68[/B]

The basketball team is selling candy as a fundraiser. A regular candy bar cost 0.75 and a king sized

The basketball team is selling candy as a fundraiser. A regular candy bar cost 0.75 and a king sized candy bar costs 1.50. In the first week of the sales the team made 36.00. Exactly 12 regular sized bars were sold that week. How many king size are left?
Let r be the number of regular bars and k be the number of king size bars. Set up our equations:
[LIST=1]
[*]0.75r + 1.5k = 36
[*]r = 12
[/LIST]
[U]Substitute (2) into (1)[/U]
0.75(12) + 1.5k = 36
9 + 1.5k = 36
[U]Use our equation solver, we get:[/U]
[B]k = 18[/B]

The bigger of 2 numbers in 5 larger than the smaller. Twice the smaller, increased by, twice the lar

The bigger of 2 numbers in 5 larger than the smaller. Twice the smaller, increased by, twice the larger, is equal to 50. Find each number.
Let the big number be b. Let the small number be s. We're given two equations:
[LIST=1]
[*]b = s + 5
[*]2s + 2b = 50
[/LIST]
Substitute equation (1) into equation (2)
2s + 2(s + 5) = 50
[URL='https://www.mathcelebrity.com/1unk.php?num=2s%2B2%28s%2B5%29%3D50&pl=Solve']Type this equation into our search engine[/URL], and we get:
[B]s = 10[/B]
Now substitute s = 10 into equation (1) to solve for b:
b = 10 + 5
[B]b = 15[/B]

The bill for the repair of a car was $294. The cost of parts was $129, and labor charge was $15 per

The bill for the repair of a car was $294. The cost of parts was $129, and labor charge was $15 per hour. How many hours did it take to repair the car? Write a sentence as your answer.
Let h be the number of hours. We have:
15h + 129 = 294
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=15h%2B129%3D294&pl=Solve']type it in the search engine [/URL]and we get:
h = [B]11[/B]

The bill from your plumber was $134. The cost for labor was $32 per hour. The cost materials was $46

The bill from your plumber was $134. The cost for labor was $32 per hour. The cost materials was $46. How many hours did the plumber work?
Set up the cost equation where h is the number of hours worked:
32h + 46 = 134
[URL='https://www.mathcelebrity.com/1unk.php?num=32h%2B46%3D134&pl=Solve']Typing this equation into our search engine[/URL], we get [B]h = 2.75[/B].

The blue star publishing company produces daily "Star news". It costs $1200 per day to operate regar

The blue star publishing company produces daily "Star news". It costs $1200 per day to operate regardless of whether any newspaper are published. It costs 0.20 to publish each newspaper. Each daily newspaper has $850 worth of advertising and each newspaper is sold for $.30. Find the number of newspaper required to be sold each day for the Blue Star company to 'break even'. I.e all costs are covered.
Build our cost function where n is the number of newspapers sold:
C(n) = 1200+ 0.2n
Now build the revenue function:
R(n) = 850 + 0.3n
Break even is where cost and revenue are equal, so set C(n) = R(n)
1200+ 0.2n = 850 + 0.3n
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=1200%2B0.2n%3D850%2B0.3n&pl=Solve']equation solver[/URL], we get:
[B]n = 3,500[/B]

The Canucks lost 6 of their first 24 games. At this rate how many would the lose in an 84 game sched

The Canucks lost 6 of their first 24 games. At this rate how many would the lose in an 84 game schedule?
Set up a proportion of losses to games where l is the number of losses for 84 games:
6/24 = l/84
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=l&den1=24&den2=84&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
l = [B]21[/B]

The charge to rent a trailer is $30 for up to 2 hours plus $9 per additional hour or portion of an

The charge to rent a trailer is $30 for up to 2 hours plus $9 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.4 hours, 3 hours, and 8.5 hours.
Set up the cost function C(h), where h is the number of hours to rent the trailer. We have, for any hours greater than 2:
C(h) = 30 + 9(h - 2)
Simplified, we have:
C(h) = 9h - 18 + 30
C(h) = 9h + 12
The question asks for C(2.4), C(3), and C(8.5)
[U]Find C(2.4)[/U]
C(2.4) = 9(2.4) + 12
C(2.4) = 21.6 + 12
C(2.4) = [B]33.6
[/B]
[U]Find C(3)[/U]
C(3) = 9(3) + 12
C(3) = 27 + 12
C(2.4) = [B][B]39[/B][/B]
[U]Find C(8.5)[/U]
C(8.5) = 9(8.5) + 12
C(8.5) = 76.5 + 12
C(8.5) = [B]88.5[/B]

The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the

The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the total cost to park for 5 hours?
Set up our equation where C is cost and h is the number of hours used to park
C = 1.5h + 2.25
With h = 5, we have:
C = 1.5(5) + 2.25
C = 7.5 + 2.25
C = 9.75

The cost of a field trip is $220 plus $7 per student. If the school can spend at most $500, how many

The cost of a field trip is $220 plus $7 per student. If the school can spend at most $500, how many students can go on the field trip?
Set up the inequality where s is the number of students:
C(s) = 220 + 7s
We want C(s) <= 500, since at most means no more than
220 + 7s <= 500
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=220%2B7s%3C%3D500&pl=Solve']inequality calculator[/URL], we get:
[B]s <= 40[/B]

The cost of a taxi ride is $1.2 for the first mile and $0.85 for each additional mile or part thereo

The cost of a taxi ride is $1.2 for the first mile and $0.85 for each additional mile or part thereof. Find the maximum distance we can ride if we have $20.75.
We set up the cost function C(m) where m is the number of miles:
C(m) = Cost per mile after first mile * m + Cost of first mile
C(m) = 0.8(m - 1) + 1.2
C(m) = 0.8m - 0.8 + 1.2
C(m) = 0.8m - 0.4
We want to know m when C(m) = 20.75
0.8m - 0.4 = 20.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.8m-0.4%3D20.75&pl=Solve']Typing this equation into our math engine[/URL], we get:
m = 26.4375
The maximum distance we can ride in full miles is [B]26 miles[/B]

The cost of hiring a car for a day is $60 plus 0.25 cents per kilometer. Michelle travels 750 kilome

The cost of hiring a car for a day is $60 plus 0.25 cents per kilometer. Michelle travels 750 kilometers. What is her total cost
Set up the cost function C(k) where k is the number of kilometers traveled:
C(k) = 60 + 0.25k
The problem asks for C(750)
C(750) = 60 + 0.25(750)
C(750) = 60 + 187.5
C(750) = [B]247.5[/B]

The cost of tuition at Johnson Community College is $160 per credit hour. Each student also has to p

The cost of tuition at Johnson Community College is $160 per credit hour. Each student also has to pay $50 in fees. Model the cost, C, for x credit hours taken.
Set up cost equation, where h is the number of credit hours:
[B]C = 50 + 160h[/B]

the cost of x concert tickets if one concert ticket costs $97

the cost of x concert tickets if one concert ticket costs $97
The cost function C(x), where x is the number of concert tickets is:
[B]C(x) = 97x[/B]

The cost of x ice cream if one ice cream cost $9 and the fixed cost is $8142

The cost of x ice cream if one ice cream cost $9 and the fixed cost is $8142
Cost function is C(x) is:
C(x) = Cost per ice cream * number of ice creams + Fixed Cost
C(x) = [B]9x + 8142[/B]

The cost of x textbooks if one textbook costs $140

The cost of x textbooks if one textbook costs $140.
Set up a cost function where x is the number of textbooks:
[B]C(x) = 140x[/B]

The cost to rent a construction crane is 450 per day plus 150 per hour. What is the maximum number o

The cost to rent a construction crane is 450 per day plus 150 per hour. What is the maximum number of hours the crane can be used each day if the rental cost is not to exceed 1650 per day?
Set up the cost function where h is the number of hours:
C(h) = 150h + 450
We want C(h) <= 1650:
150h + 450 <= 1650
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=150h%2B450%3C%3D1650&pl=Solve']equation/inequality solver[/URL], we get:
[B]h <= 8[/B]

The dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for each

The dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for each ticket sold they sell to the Spring Fling dance. The dance will cost $400
Let t be the number of tickets sold. We have a Revenue function R(t):
R(t) = 4t + 72
We want to know t such that R(t) = 400. So we set R(t) = 400:
4t + 72 = 400
[URL='https://www.mathcelebrity.com/1unk.php?num=4t%2B72%3D400&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]t = 82[/B]

The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. Wh?

The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. What are the numbers?
Let the smaller number be x. Let the larger number be y. We're given:
[LIST=1]
[*]y - x = 108
[*]6x = y + 2
[/LIST]
Rearrange (1) by adding x to each side:
[LIST=1]
[*]y = x + 108
[/LIST]
Substitute this into (2):
6x = x + 108 + 2
Combine like terms
6x = x +110
Subtract x from each side:
5x = 110
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D110&pl=Solve']Plugging this equation into our search engine[/URL], we get:
x = [B]22[/B]

the difference between 7 times a number and 9 less than a number

the difference between 7 times a number and 9 less than a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
7 times a number means we multiply x by 7
7x
9 less than a number means we subtract 9 from x
x - 9
The difference between the two expressions means we subtract (x - 9) from 7x
7x - (x - 9)
Simplifying this, we have:
7x - x + 9
Grouping like terms, we get:
[B]6x + 9[/B]

The difference between a number and 9 is 27. Find that number

The difference between a number and 9 is 27. Find that number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The difference between a number and 9
x - 9
The word [I]is[/I] means equal to, so we set x - 9 equal to 27:
x - 9 = 27
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-9%3D27&pl=Solve']type it in our math engine[/URL] and we get:
x = [B]36[/B]

The difference between the opposite of a number and 6.

The difference between the opposite of a number and 6.
The phrase [I]a number means[/I] an arbitrary variable, let's call it x.
x
The opposite of a number means we multiply by x by -1
-x
The phrase [I]the difference between[/I] means we subtract 6 from -x:
[B]-x - 6[/B]

The difference between the product of 4 and a number and the square of a number

The difference between the product of 4 and a number and the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The product of 4 and a number:
4x
The square of a number means we raise x to the power of 2:
x^2
The difference between the product of 4 and a number and the square of a number:
[B]4x - x^2[/B]

the difference between triple a number and double a number

the difference between triple a number and double a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Triple a number means we multiply x by 3:
3x
Double a number means we multiply x by 2:
2x
The difference means we subtract 2x from 3x:
3x - 2x
Simplifying like terms, we have:
(3 - 2)x = [B]x[/B]

The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is

The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number
Let the smaller number be s. Let the larger number be l. We're given two equations:
[LIST=1]
[*]l - s = 25
[*]s = l/6
[/LIST]
Plug in equation (2) into equation (1):
l - l/6 = 25
Multiply each side of the equation by 6 to remove the fraction:
6l - l = 150
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=6l-l%3D150&pl=Solve']type this equation into our search engine[/URL] and we get:
l = 30
To solve for s, we plug in l = 30 into equation (2) above:
s = 30/6
[B]s = 5[/B]

The difference between two numbers is 96. One number is 9 times the other. What are the numbers?

The difference between two numbers is 96. One number is 9 times the other. What are the numbers?
Let x be the first number
Let y be the second number
We're given two equations:
[LIST=1]
[*]x - y = 96
[*]x = 9y
[/LIST]
Substitute equation (2) into equation (1) for x
9y - y = 96
[URL='https://www.mathcelebrity.com/1unk.php?num=9y-y%3D96&pl=Solve']Plugging this equation into our math engine[/URL], we get:
y = [B]12
[/B]
If y = 12, then we plug this into equation 2:
x = 9(12)
x = [B]108[/B]

The difference between two positive numbers is 5 and the square of their sum is 169

The difference between two positive numbers is 5 and the square of their sum is 169.
Let the two positive numbers be a and b. We have the following equations:
[LIST=1]
[*]a - b = 5
[*](a + b)^2 = 169
[*]Rearrange (1) by adding b to each side. We have a = b + 5
[/LIST]
Now substitute (3) into (2):
(b + 5 + b)^2 = 169
(2b + 5)^2 = 169
[URL='https://www.mathcelebrity.com/community/forums/calculator-requests.7/create-thread']Run (2b + 5)^2 through our search engine[/URL], and you get:
4b^2 + 20b + 25
Set this equal to 169 above:
4b^2 + 20b + 25 = 169
[URL='https://www.mathcelebrity.com/quadratic.php?num=4b%5E2%2B20b%2B25%3D169&pl=Solve+Quadratic+Equation&hintnum=+0']Run that quadratic equation in our search engine[/URL], and you get:
b = (-9, 4)
But the problem asks for [I]positive[/I] numbers. So [B]b = 4[/B] is one of our solutions.
Substitute b = 4 into equation (1) above, and we get:
a - [I]b[/I] = 5
[URL='https://www.mathcelebrity.com/1unk.php?num=a-4%3D5&pl=Solve']a - 4 = 5[/URL]
[B]a = 9
[/B]
Therefore, we have [B](a, b) = (9, 4)[/B]

The difference of 2 positive numbers is 54. The quotient obtained on dividing the 1 by the other is

The difference of 2 positive numbers is 54. The quotient obtained on dividing the 1 by the other is 4. Find the numbers.
Let the numbers be x and y. We have:
[LIST]
[*]x - y = 54
[*]x/y = 4
[*]Cross multiply x/y = 4 to get x = 4y
[*]Now substitute x = 4y into the first equation
[*](4y) - y = 54
[*]3y = 54
[*]Divide each side by 3
[*][B]y = 18[/B]
[*]If x = 4y, then x = 4(18)
[*][B]x = 72[/B]
[/LIST]

The difference of 25 and a number added to triple another number

The difference of 25 and a number added to triple another number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x:
x
The difference of 25 and a number means we subtract x from 25:
25 - x
The phrase [I]another number[/I] means a different arbitrary variable, let's call it y:
y
Triple another number means we multiply y by 3:
3y
The phrase [I]added to[/I] means we add 25 - x to 3y
[B]25 - x + 3y[/B]

the difference of 4 and the quotient of 18 and a number

the difference of 4 and the quotient of 18 and a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The quotient of 18 and a number means we divide 18 by the variable x.
18/x
The difference of 4 and the quotient above means we subtract 18/x from 4:
[B]4 - 18/x[/B]

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the num

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?
We have two expressions:
[U]Expression 1: [I]The difference of a number and 6[/I][/U]
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The difference of a number and 6 means we subtract 6 from x:
x - 6
[U]Expression 2: [I]5 times the sum of the number and 2[/I][/U]
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The sum of a number and 2 means we add 2 to x:
x + 2
5 times the sum means we multiply x + 2 by 5
5(x + 2)
[U]For the last step, we evaluate the expression [I]is the same as[/I][/U]
This means equal to, so we set x - 6 equal to 5(x + 2)
[B]x - 6 = 5(x + 2)[/B]

The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown n

The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown number.
The phrase a number uses the variable w.
3 times w is written as 3w
The difference of 3w and 6 is written as 3w - 6
Set this equal to 7
[B]3w - 6 = 7
[/B]
This is our algebraic expression. To solve this equation for w, we [URL='http://www.mathcelebrity.com/1unk.php?num=3w-6%3D7&pl=Solve']type the algebraic expression into our search engine[/URL].

The difference of twice a number and 4 is at least -27

The difference of twice a number and 4 is at least -27.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Twice a number means multiply the number by 2
2x
[I]and 4[/I] means we add 4 to our expression:
2x + 4
[I]Is at least[/I] means an inequality. In this case, it's greater than or equal to:
[B]2x + 4 >= -27
[/B]
To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B4%3E%3D-27&pl=Solve']type it in the search engine[/URL].

The difference of twice a number and 6 is at most 28

The difference of twice a number and 6 is at most 28
This is an algebraic expression. Let's take it in parts:
[LIST=1]
[*]The phrase [I]a number[/I], means an arbitrary variable, let's call it x
[*]Twice this number means we multiply x by 2: 2x
[*][I]The difference of[/I] means subtract, so we subtract 6 to 2x: 2x - 6
[*][I]Is at most [/I]means less than or equal to, so we create an inequality where 2x - 6 is less than or equal to 28, using the <= sign
[/LIST]
[B]2x - 6 <= 28
[/B]
If you wish to solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-6%3C%3D28&pl=Solve']click this link[/URL].

the difference of twice a number and 8 is at most -30

the difference of twice a number and 8 is at most -30.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Twice this number means we multiply by 2, so we have 2x.
We take the difference of 2x and 8, meaning we subtract 8:
2x - 8
Finally, the phrase [I]at most[/I] means an inequality, also known as less than or equal to:
[B]2x - 8 <= 30 <-- This is our algebraic expression
[/B]
To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x-8%3C%3D30&pl=Solve']type it into the search engine[/URL] and get x <= 19.

The difference of twice a number and 9 is less than 22

The difference of twice a number and 9 is less than 22
The phrase a number, means an arbitrary variable, let's call it x.
x
Twice a number
2x
The difference of twice a number and 9
2x - 9
Is less than 22
[B]2x - 9 < 22[/B]

The difference of two numbers is 12 and their mean is 15. Find the two numbers

The difference of two numbers is 12 and their mean is 15. Find the two numbers.
Let the two numbers be x and y. We're given:
[LIST=1]
[*]x - y = 12
[*](x + y)/2 = 15. <-- Mean is an average
[/LIST]
Rearrange equation 1 by adding y to each side:
x - y + y = y + 12
Cancelling the y's on the left side, we get:
x = y + 12
Now substitute this into equation 2:
(y + 12 + y)/2 = 15
Cross multiply:
y + 12 + y = 30
Group like terms for y:
2y + 12 = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B12%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 9[/B]
Now substitute this into modified equation 1:
x = y + 12
x = 9 + 12
[B]x = 21[/B]

The difference of two numbers is 720. The smaller of the numbers is 119. What is the other number?

The difference of two numbers is 720. The smaller of the numbers is 119. What is the other number?
Let the larger number be l. We're given:
l - 119 = 720
[URL='https://www.mathcelebrity.com/1unk.php?num=l-119%3D720&pl=Solve']We type this equation into the search engine[/URL] and we get:
l = [B]839[/B]

The domain of a relation is all even negative integers greater than -9. The range y of the relation

The domain of a relation is all even negative integers greater than -9. The range y of the relation is the set formed by adding 4 to the numbers in the domain. Write the relation as a table of values and as an equation.
The domain is even negative integers greater than -9:
{-8, -6, -4, -2}
Add 4 to each x for the range:
{-8 + 4 = -4, -6 + 4 = -2. -4 + 4 = 0, -2 + 4 = 2}
For ordered pairs, we have:
(-8, -4)
(-6, -2)
(-4, 0)
(-2, 2)
The equation can be written:
y = x + 4 on the domain (x | x is an even number where -8 <= x <= -2)

The enrollment at High School R has been increasing by 20 students per year. High School R currently

The enrollment at High School R has been increasing by 20 students per year. High School R currently has 200 students. High School T has 400 students and is decreasing 30 students per year. When will the two school have the same enrollment of students?
Set up the Enrollment function E(y) where y is the number of years.
[U]High School R:[/U]
[I]Increasing[/I] means we add
E(y) = 200 + 20y
[U]High School T:[/U]
[I]Decreasing[/I] means we subtract
E(y) = 400 - 30y
When the two schools have the same enrollment, we set the E(y) functions equal to each other
200 + 20y = 400 - 30y
To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=200%2B20y%3D400-30y&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]4[/B]

The entrance fee to the national park is $30. A campsite fee is $15 per night. Write an equation to

The entrance fee to the national park is $30. A campsite fee is $15 per night. Write an equation to represent the situation.
Let n be the number of nights. We have a cost (C) of:
C = Cost per night * n + entrance fee
C = [B]15n + 50[/B]

the equation of a line is y = mx + 4. find m if the line passes through (-5,0)

the equation of a line is y = mx + 4. find m if the line passes through (-5,0)
Plug in our numbers of x = -5, and y = 0:
-5m + 4 = 0
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=-5m%2B4%3D0&pl=Solve']plug in this equation into our search engine[/URL] and we get:
[B]m = 0.8 or 4/5[/B]
so our line equation becomes:
[B]y = 4/5x + 4[/B]

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered t

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 231 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer.
Digit, Probability
1, 0.301
2, 0.176
3, 0.125
4, 0.097
5, 0.079
6, 0.067
7, 0.058
8, 0.051
9, 0.046
[B][U]Fradulent Checks[/U][/B]
Digit, Frequency
1, 36
2, 32
3, 45
4, 20
5, 24
6, 36
7, 15
8, 16
9, 7
Complete parts (a) and (b).
(a) Using the level of significance α = 0.05, test whether the first digits in the allegedly fraudulent checks obey Benford's Law. Do the first digits obey the Benford's Law?

Yes or No Based on the results of part (a), could one think that the employe is guilty of embezzlement? Yes or No Show frequency percentages Digit Fraud Probability Benford Probability 1 0.156 0.301 2 0.139 0.176 3 0.195 0.125 4 0.087 0.097 5 0.104 0.079 6 0.156 0.067 7 0.065 0.058 8 0.069 0.051 9 0.03 0.046 Take the difference between the 2 values, divide it by the Benford's Value. Sum up the squares to get the Test Stat of 2.725281277 Critical Value Excel: =CHIINV(0.95,8) = 2.733 Since test stat is less than critical value, we cannot reject, so [B]YES[/B], it does obey Benford's Law and [B]NO[/B], there is not enough evidence to suggest the employee is guilty of embezzlement.

Yes or No Based on the results of part (a), could one think that the employe is guilty of embezzlement? Yes or No Show frequency percentages Digit Fraud Probability Benford Probability 1 0.156 0.301 2 0.139 0.176 3 0.195 0.125 4 0.087 0.097 5 0.104 0.079 6 0.156 0.067 7 0.065 0.058 8 0.069 0.051 9 0.03 0.046 Take the difference between the 2 values, divide it by the Benford's Value. Sum up the squares to get the Test Stat of 2.725281277 Critical Value Excel: =CHIINV(0.95,8) = 2.733 Since test stat is less than critical value, we cannot reject, so [B]YES[/B], it does obey Benford's Law and [B]NO[/B], there is not enough evidence to suggest the employee is guilty of embezzlement.

The fixed costs to produce a certain product are 15,000 and the variable costs are $12.00 per item.

The fixed costs to produce a certain product are 15,000 and the variable costs are $12.00 per item. The revenue for a certain product is $27.00 each. If the company sells x products, then what is the revenue equation?
R(x) = Revenue per item x number of products sold
[B]R(x) = 27x[/B]

The flu is starting to hit Lanberry. Currently, there are 894 people infected, and that number is gr

The flu is starting to hit Lanberry. Currently, there are 894 people infected, and that number is growing at a rate of 5% per day. Overall, how many people will have gotten the flu in 5 days?
Our exponential equation for the Flu at day (d) is:
F(d) = Initial Flu cases * (1 + growth rate)^d
Plugging in d = 5, growth rate of 5% or 0.05, and initial flu cases of 894 we have:
F(5) = 894 * (1 + 0.05)^5
F(5) = 894 * (1.05)^5
F(5) = 894 * 1.2762815625
F(5) = [B]1141[/B]

the fuel tank of a jet used gas at a constant rate of 300 gallons for each hour of flight. the tank

the fuel tank of a jet used gas at a constant rate of 300 gallons for each hour of flight. the tank can hold a maximum of 2400 gallons of gas. write an equation representing the amount of fuel left in the tank as a function of the number of hours spent flying.
We have an equation F(h) where h is the number of hours since the flight took off:
[B]F(h) = 2400 - 300h[/B]

the grass in jamie’s yard grew 16 centimeters in 10 days. how many days did it take for the grass to

the grass in jamie’s yard grew 16 centimeters in 10 days. how many days did it take for the grass to grow 1 centimeter
We set up a proportion of centimeters to days where d is the number of days it takes for the grass to grow 1 centimeter:
16/10 = 1/d
To solve this proportion for d, [URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=1&den1=10&den2=d&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
d = [B]0.625 or 5/8[/B]

The Lakewood library has $8,040 to buy science magazines. If each magazine costs $3, how many magazi

The Lakewood library has $8,040 to buy science magazines. If each magazine costs $3, how many magazines will the library be able to buy?
Let number of magazines be m. We know that:
Cost per magazine * m = Total Cost
We're given Total Cost = 8040 and Cost per magazine = 3, so we have
3m = 8040
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%3D8040&pl=Solve']type it in our math engine[/URL] and we get:
m = [B]2680[/B]

The larger number b exceeds the smaller number c by 45.

The larger number b exceeds the smaller number c by 45.
Exceeds means greater than or more than, so we have:
[B]b = c + 45[/B]

The larger of 2 numbers is 1 more than 3 times the smaller number

The larger of 2 numbers is 1 more than 3 times the smaller number.
Let the larger number be l. Let the smaller number be s. The algebraic expression is:
3 times the smaller number is written as:
3s
1 more than that means we add 1
3s + 1
Our final algebraic expression uses the word [I]is[/I] meaning an equation. So we set l equal to 3s + 1
[B]l = 3s + 1[/B]

The largest