set - a collection of different things; a set contains elements or members, which can be mathematical objects of any kind

$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]

π Digits

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

(A intersection B) U (A intersection B')

(A intersection B) U (A intersection B')
This is the [B]Universal Set U[/B].
Everything that isn't A and isn't B is everything else.

(A^C)^C

(A^C)^C
we read this as The complement of the Complement of Set A
The complement of set A is anything NOT in A.
But the complement of the complement is anything NOT NOT IN A.
Which is just [B]A
[MEDIA=youtube]-eo-Bq6qZVM[/MEDIA][/B]

-2 <= x +4 < 9

-2 <= x +4 < 9
Subtract 4 from each piece:
-2 - 4 <= x < 5
Simplify:
[B]-6 <= x < 5
[/B]
To find the interval notation, we set up our notation:
[LIST]
[*]The left side has a solid bracket, since we have an equal sign:
[*]The right side has an open parentheses, since we have no equal sign
[*][B][-6, 5)[/B]
[/LIST]

-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]

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 person is born every 5 seconds. How many people are born in 1 minute?

1 person is born every 5 seconds. How many people are born in 1 minute?
Set up the chain:
1 person / 5 seconds * 60 seconds / 1 minute
Since 60/5 is 12, and the seconds cancel, we have:
[B]12 people / minute[/B]

1/2 of x and 10 is 30. Find the x.

1/2 of x and 10 is 30. Find the x.
x and 10 means we add:
x + 10
1/2 of this:
1/2(x + 10)
The phrase is means equal to, so we set 1/2(x + 10) equal to 30 for our algebraic expression
[B]1/2(x + 10) = 30[/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 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]

1/3 times q plus 5 equal q minus 4

1/3 times q plus 5 equal q minus 4
1/3 times q plus 5:
(q + 5)/3
q minus 4:
q - 4
The word [I]equal[/I] means we set (q + 5)/3 equal to q - 4:
[B](q + 5)/3 = q - 4[/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]

10 is twice the sum of x and 5

10 is twice the sum of x and 5
The sum of x and 5 means we add:
x + 5
Twice the sum means we multiply by 2:
2(x + 5)
The word [I]is[/I] means an equation, so we set 2(x + 5) equal to 10
[B]2(x + 5) = 10[/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

104 subtracted from the quantity 6 times r is the same as r

104 subtracted from the quantity 6 times r is the same as r
The quantity 6 times r means we multiply 6 by r:
6r
104 subtracted from 6r is written as:
6r - 104
[B]The phrase [I]is the same as[/I] means we have an equation. So we set 6r - 104 equal to r
6r - 104 = r[/B]

108 times a, reduced by 147 is k subtracted from 56

108 times a, reduced by 147 is k subtracted from 56
Take this algebraic expression in pieces:
Step 1: 108 times a:
108a
Step 2: Reduced by means subtract, so we subtract 47 from 108a:
108a - 47
Step 3: ksubtracted from 56:
56 - k
Step 4: The phrase [I]is[/I] means equal to, so we set 108a - 47 equal to 56 - k
[B]108a - 47 = 56 - k
[MEDIA=youtube]KrY6uzKeeB0[/MEDIA][/B]

110 subtracted from the product of 244 and w is the product of r and 177 increased by 266

110 subtracted from the product of 244 and w is the product of r and 177 increased by 266
The product of 244 and w:
244w
110 subtracted from the product of 244 and w
244w - 110
the product of r and 177
177r
the product of r and 177 increased by 266
177r + 266
The word [I]is[/I] means equal to, so we set 244w - 110 equal to 177r + 266
[B]244w - 110 = 177r + 266[/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

13 is the product of 5p and 5

13 is the product of 5p and 5
the product of 5p and 5 means we multiply 5p by 5:
5p * 5
25p
The word [I]is[/I] means equal to, so we set 25p equal to 13
[B]13 = 25p
25p = 13[/B]

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]

132 is 393 multiplied by y

132 is 393 multiplied by y
393 multiplied by y
393y
The word [I]is[/I] means equal to, so we set 393y equal to 132 as our algebraic expression
[B]393y = 132
[/B]
If you need to solve for y, use our [URL='http://www.mathcelebrity.com/1unk.php?num=393y%3D132&pl=Solve']equation calculator[/URL]

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 cats, 10 have stripes, 7 have stripes and green eyes, how many cats have just green eyes

Let G be green eyes and S be Stripes, and SG be Stripes and Green Eyes.
[U]Set up an equation[/U]
Total Cats = Green Eyes + Stripes - Green Eyes and Stripes
15 = G + 10 - 7
15 = G + 3
[U]Subtract 3 from each side:[/U]
[B]G = 12[/B]

15 minus twice a equals b

15 minus twice a equals b
Twice a means we multiply a by 2:
2a
15 minus 2a:
15 - 2a
Set this equalto b:
[B]15 - 2a = b[/B]

17 decreased by three times d equals c

17 decreased by three times d equals c
three times d means we multiply d by 3:
3d
17 decreased by three times d means we subtract 3d from 17
17 - 3d
The word [I]equals[/I] means an equation, so we set 17 - 3d equal to c:
[B]17 - 3d = c[/B]

175 students separated into n classes is 25

175 students separated into n classes is 25
[U]Divide 175 by n[/U]
175/n
[U]The word [I]is[/I] means equal to, so set this expression equal to 25[/U]
175/n = 25
[U]Cross multiply[/U]
25n = 175
[U]Divide each side by 25[/U]
[B]n = 7[/B]

18 divided by the difference of t and 9

The difference of t and 9 is:
t - 9
Now, we set up a quotient with 18 as the numerator and t - 9 as the denominator
18
------
t - 9

2 Asset Portfolio

Given a portfolio with 2 assets, this determines the expected return (mean), variance, and volatility (standard deviation) of the portfolio.

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 consecutive even integers that equal 118

Let x be the first even integer. That means the next consecutive even integer must be x + 2.
Set up our equation:
x + (x + 2) = 118
Group x terms
2x + 2 = 118
Subtract 2 from each side
2x = 116
Divide each side by 2
x = 58
Which means the next consecutive even integer is 58 + 2 = 60
So our two consecutive even integers are [B]58, 60[/B]
Check our work:
58 + 60 = 118

2 less than 3 times n is 4 more than n

2 less than 3 times n is 4 more than n
3 times n:
3n
2 less than 3 times n
3n - 2
4 more than n:
n + 4
The word [I]is[/I] means equal to, so we set 3n - 2 equal to n + 4:
[B]3n - 2 = n + 4[/B]

2 pens and 1 eraser cost $35 and 3 pens and 4 erasers cost $65. X represents the cost of 1 pen and Y

2 pens and 1 eraser cost $35 and 3 pens and 4 erasers cost $65. X represents the cost of 1 pen and Y represents the cost of 1 eraser. Write the 2 simultaneous equations and solve.
Set up our 2 equations where cost = price * quantity:
[LIST=1]
[*]2x + y = 35
[*]3x + 4y = 65
[/LIST]
We can solve this one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]x (cost of 1 pen) = 15[/B]
[*][B]y (cost of 1 eraser) = 5[/B]
[/LIST]

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 the quantity x minus 1 is 12

2 times the quantity x minus 1 is 12
The quantity x minus 1 is written as:
x - 1
2 times this quantity:
2(x - 1)
The word [I]is[/I] means an equation, so we set 2(x - 1) equal to 12:
[B]2(x - 1) = 12[/B]

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 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 tons of dirt cost $280.00. What is the price per pound?

2 tons of dirt cost $280.00. What is the price per pound?
We know that 1 ton = 2000 pounds.
So 2 tons = 2*2000 = 4,000 pounds
We rewrite this as 4,000 pounds of dirt cost $280.00.
We set up a proportion where p is the price per one pound:
4000/280 = 1/p
[URL='https://www.mathcelebrity.com/prop.php?num1=4000&num2=1&den1=280&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Plugging this in our search engine[/URL], we get:
p = [B]0.07 or 7 cents per pound.[/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]

217 times u, reduced by 180 is the same as q

217 times u, reduced by 180 is the same as q.
Take this algebraic expression pieces:
Step 1: 217 times u
We multiply the variable u by 217
217u
Step 2: reduced by 180
Subtract 180 from 217u
217u - 180
The phrase [I]is the same as[/I] means an equation, so we set 217u - 180 equal to q
[B]217u - 180 = q[/B]

223 subtracted from the quantity 350 times a is equal to b

223 subtracted from the quantity 350 times a is equal to b
Take this algebraic expression in parts:
[LIST]
[*]the quantity 350 times a: 350a
[*]223 subtracted from the quantity: 350a - 223
[*]The phrase [I]is equal to[/I] means an equation, so we set 350a - 223 equal to b
[/LIST]
[B]350a - 223 = b[/B]

23 decreased by thrice of y is not equal to 15

Thrice of y means multiply y by 3
3y
23 decreased by 3y means we subtract
23 - 3y
Is not equal to means we set up an equation with not equal sign
23 - 3y <> 15

231 is 248 subtracted from the quantity h times 128

231 is 248 subtracted from the quantity h times 128
Let's take this algebraic expression in parts:
[LIST=1]
[*]h times 128: 128h
[*]24 subtracted from this: 128h - 248
[*]The word [I]is[/I] means an equation, so we set 128h - 248 equal to 231
[/LIST]
[B]128h - 248 = 231[/B] <-- This is our algebraic expression
If the problem asks you to solve for h, then you [URL='https://www.mathcelebrity.com/1unk.php?num=128h-248%3D231&pl=Solve']type in this equation into our search engine[/URL] and get:
h = [B]3.742[/B]

249 equals 191 times c, decreased by 199

249 equals 191 times c, decreased by 199
[U]Take this in pieces:[/U]
191 times c: 191c
The phrase [I]decreased by[/I] means we subtract 199 from 191c: 191c - 199
We set this expression equal to 249:
[B]191c - 199 = 249[/B] <-- This is our algebraic expression
If you want to solve for c, type this equation into the search engine and we get:
[B]c = 2.346[/B]

298 is the same as c and 230 more

[I]Is the same as[/I] means equal to. 230 more means we add 230.
Set up this equation:
c + 230 = 298
To solve for c if needed, visit our [URL='http://www.mathcelebrity.com/1unk.php?num=c%2B230%3D298&pl=Solve']calculator[/URL].
c = 68

2x decreased by 15 is equal to -27

2x decreased by 15 is equal to -27
The phrase [I]decreased by[/I] 15 means we subtract 15 from 2x:
2x - 15
The phrase [I]is equal to[/I] means an equation, so we set 2x - 15 equal to -27
[B]2x - 15 = -27 [/B] <-- This is our algebraic expression
To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D-27&pl=Solve']type 2x - 15 = -27 into the search engine[/URL].

2x plus 4 increased by 15 is 57

2x plus 4 increased by 15 is 57
Take this algebraic expression in parts:
[LIST]
[*]2x plus 4: 2x + 4
[*][I]Increased by[/I] means we add 15 to 2x + 4: 2x + 4 + 15 = 2x + 19
[*]The word [I]is[/I] means an equation, so we set 2x + 19 equal to 57:
[/LIST]
Our final algebraic expression is:
[B]2x + 19 = 57
[/B]
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B19%3D57&pl=Solve']type this equation into our search engine [/URL]and we get
x = [B]19[/B]

3 cartons of eggs for $5 what if the cost of 8 cartons

3 cartons of eggs for $5 what if the cost of 8 cartons
Set up a proportion of cartons of eggs to price where p is the price of 8 cartons:
3/5 = 8/p
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=8&den1=5&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get:
p = [B]13.33[/B]

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 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 difference of a and b is equal to 4 times c

3 times the difference of a and b is equal to 4 times c
[U]The difference of a and b:[/U]
a - b
[U]3 times the difference of a and b:[/U]
3(a - b)
[U]4 times c:[/U]
4c
The phrase [I]is equal to[/I] means an equation. So we set 3(a - b) equal to 4c:
[B]3(a - b) = 4c[/B]

3 times the difference of x and 5 is 15

The difference of x and 5 means we subtract:
x - 5
3 times the difference means we multiply (x - 5) by 3
3(x - 5)
Is, means equal to, so we set our expression equal to 15
[B]3(x - 5) = 15
[/B]
If you need to take it one step further to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3%28x-5%29%3D15&pl=Solve']equation calculator[/URL]

3 times the quantity 2 decreased by x is 9

3 times the quantity 2 decreased by x is 9
The quantity 2 decreased by x. The phrase [I]decreased by[/I] means we subtract:
2 - x
3 times the quantity:
3(2 - x)
The word [I]is[/I] means equal to, so we set 3(2 - x) equal to 9:
[B]3(2 - x) = 9
[MEDIA=youtube]Hzyt_GajZA4[/MEDIA][/B]

3 times the sum of 2 decreased by x is 9

3 times the sum of 2 decreased by x is 9
2 decreased by x:
2 - x
3 times the sum means we multiply 2 - x by 3:
3(2 - x)
The phrase [I]is 9[/I] means equal to, so we set 3(2 - x) equal to 9:
[B]3(2 - x) = 9[/B]

3 times x minus y is 5 times the sum of y and 2 times x

3 times x minus y is 5 times the sum of y and 2 times x
Take this algebraic expression in pieces:
3 times x:
3x
Minus y means we subtract y from 3x
3x - y
The sum of y and 2 times x mean we add y to 2 times x
y + 2x
5 times the sum of y and 2 times x:
5(y + 2x)
The word [I]is[/I] means an equation, so we set 3x - y equal to 5(y + 2x)
[B]3x - y = 5(y + 2x)[/B]

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]

30 is equal to thrice y decreased by z

30 is equal to thrice y decreased by z
Thrice y means we multiply y by 3:
3y
Decreased by z means we subtract z from 3y
3y - z
The phrase [I]is[/I] means an equal to, so we set up an equation where 3y - z is equal to 30
[B]3y - z = 30[/B]

300 reduced by 5 times my age is 60

300 reduced by 5 times my age is 60
Let my age be a. We have:
5 times my age = 5a
300 reduced by 5 times my age means we subtract 5a from 300:
300 - 5a
The word [I]is[/I] means an equation, so we set 300 - 5a equal to 60 to get our final algebraic expression:
[B]300 - 5a = 60
[/B]
If you have to solve for a, you [URL='https://www.mathcelebrity.com/1unk.php?num=300-5a%3D60&pl=Solve']type this equation into our search engine[/URL] and you get:
a = [B]48[/B]

309 is the same as 93 subtracted from the quantity f times 123

309 is the same as 93 subtracted from the quantity f times 123.
The quantity f times 123:
123f
Subtract 93:
123f - 93
The phrase [I]is the same as[/I] means an equation, so we set 123f - 93 equal to 309
[B]123f - 93 = 309[/B] <-- This is our algebraic expression
If you wish to solve for f, [URL='https://www.mathcelebrity.com/1unk.php?num=123f-93%3D309&pl=Solve']type this equation into the search engine[/URL], and we get f = 3.2683.

324 times z, reduced by 12 is z

324 times z, reduced by 12 is z.
Take this algebraic expression in pieces:
324 [I]times[/I] z means we multiply 324 by the variable z.
324z
[I]Reduced by[/I] 12 means we subtract 12 from 324z
324z - 12
The word [I]is[/I] means we have an equation, so we set 324z - 12 equal to z
[B]324z - 12 = z [/B] <-- This is our algebraic expression

339 equals 303 times w, minus 293

339 equals 303 times w, minus 293
Take this algebraic expression in pieces:
303 times w:
303w
Minus 293:
303w - 293
The phrase [I]equals[/I] means we have an equation. We set 303w - 293 = 339
[B]303w - 293 = 339[/B] <-- This is our algebraic expression
To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=303w-293%3D339&pl=Solve']we type this equation into our search engine[/URL] to get:
[B]w = 2.086[/B]

36 PAGES AND IT 3/8CM THICK, WHAT IS THE THICKNESS OF 1 PAGE?

36 PAGES AND IT 3/8CM THICK, WHAT IS THE THICKNESS OF 1 PAGE?
Set up a proportion in pages to cm:
36 pages /3/8cm = 1 page/x cm
Cross multiply:
36x = 3/8
Divide each side by 36
x = 3/(8 * 36)
x = 1/(8*12)
x = [B]1/96 cm[/B]

3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5

3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5
This is an algebraic expression. Let's take this algebraic expression in 5 parts:
[LIST=1]
[*]The sum of 2x and 1 means we add 1 to 2x: 2x + 1
[*]2 times the sum of 2x and 1: 2(2x + 1)
[*]3x less than the sum of 2x and 1 means we subtract 3x from 2(2x + 1): 2(2x + 1) - 3x
[*]The sum of 2 and 5 means we add 5 to 2: 2 + 5
[*]Finally, the phrase [I]equal[/I] means an equation, so we set #3 equal to #4
[/LIST]
Our algebraic expression is:
[B]2(2x + 1) - 3x = 2 + 5[/B]
[B][/B]
Now, some problems may ask you to simplify. In this case, we multiply through and group like terms:
4x + 2 - 3x = 7
[B]x + 2 = 7 <-- This is our simplified algebraic expression
[/B]
Now, what if the problem asks you to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B2%3D7&pl=Solve']you type this into our search engine[/URL] and get:
x =[B] 5[/B]

3x over 27 equals 2x minus 2 over 15

3x over 27 equals 2x minus 2 over 15
3x over 27:
3x/27
2x minus 2 over 15:
(2x - 2)/15
Set them equal to each other:
3x/27 = (2x - 2)/15

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 minus 3p equals 36

4 minus 3p equals 36
4 minus 3p:
4 - 3p
The phrase [I]equals[/I] means an equation, so we set 4 - 3p equal to 36:
[B]4 - 3p = 36[/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 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

400 reduced by 3 times my age is 214

400 reduced by 3 times my age is 214
Let my age be a. We have:
3 times my age:
3a
400 reduced by 3 times my age:
400 - 3a
The word [I]is[/I] means an equation. So we set 400 - 3a equal to 214
400 - 3a = 214
Now if you want to solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D214&pl=Solve']type it in the search engin[/URL]e and we get;
a = [B]62[/B]

48 is the difference of Chrissys height and 13 .

48 is the difference of Chrissys height and 13 .
Let Chrissy's height = h.
The difference of the height and 13 is h - 13.
We set this expression equal to 48:
[B]h - 13 = 48
[/B]
Note: To solve this, [URL='http://www.mathcelebrity.com/1unk.php?num=h-13%3D48&pl=Solve']paste this problem into the search engine[/URL].

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 -8| -2n|=-75

Subtract 5 from each side:
-8|-2n| = -80
Divide each side by -8
|-2n| = 10
Since this is an absolute value equation, we need to setup two equations:
-2n = 10
-2n = -10
Solving for the first one by dividing each side by -2, we get:
n = -5
Solving for the second one by dividing each side by -2, we get:
n = 5

5 added to xis 11

5 added to x means we use the plus sign for a sum.
x + 5
"is" means equals, so we set that equal to 11.
x + 5 = 11 <-- This is our algebraic expression.

5 chocolates cost $25. What will 15 chocolates cost?

5 chocolates cost $25. What will 15 chocolates cost?
Set up a proportion of chocolates to cost, where p is the price of 15 chocolates:
5/25 = 15/p
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=5&num2=15&den1=25&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]p = 75[/B]

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 less than x is y

5 less than x means we subtract 5 from x.
x - 5
Is, means equal to, so we set x - 5 equal to y
x - 5 = y

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 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, 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]

50 meters in 21.81 seconds

Set up a proportion, with meters to seconds:
50 meters/21.81 seconds = x meters / 1 second
50/21.81 = x/1
Using our proportion calculator, we have:
[B]x = 2.293 meters per second[/B]

54 is the sum of 15 and Vidyas score

54 is the sum of 15 and Vidyas score.
Let Vida's score be s.
The sum of 15 and s:
s + 15
When they say "is", they mean equal to, so we set s + 15 equal to 54. Our algebraic expression is below:
[B]s + 15 = 54
[/B]
To solve this equation for s, use our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B15%3D54&pl=Solve']equation calculator[/URL]

54 is the sum of 24 and Julies score. Use the variable J to represent Julies score.

54 is the sum of 24 and Julies score. Use the variable J to represent Julies score.
Sum of 24 and Julie's score:
24 + J
The phrase [I]is[/I] means an equation, so we set 24 + J equal to 54 to get an algebraic expression:
[B]24 + J = 54[/B]

54% of students got an F, 15% of students got a D, 19% of students got a B and 12% of students got a

54% of students got an F, 15% of students got a D, 19% of students got a B and 12% of students got an A. if there were 26 students, how many got an F?
First, we check our total percentages:
54% + 15% + 19% + 12% = 100% <-- Good, we have our full sample set
F Students = 54% * 26
F Students = 14.04 -->[B] 14[/B]

55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. What is the

55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. What is the length of shadow she will cast?
Set up a proportion of height to shadow length where s is the shadow length of the woman:
55/32 = 5.5/s
[URL='https://www.mathcelebrity.com/prop.php?num1=55&num2=5.5&den1=32&den2=s&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
s = [B]3.2[/B]

56 is the sum of 20 and Donnie's savings. Use the variable d to represent Donnie's savings

56 is the sum of 20 and Donnie's savings. Use the variable d to represent Donnie's savings
The sum of 20 and Donnie's savings using [I]d[/I] to represent Donnie's savings:
20 + d
The word [I]is[/I] means equal to, so we set 20 + d equal to 56:
[B]20 + d = 56[/B]

59 is the difference of vanessas height and 20

59 is the difference of vanessas height and 20.
Let h be Vanessa's height. We have the difference of h and 20:
h - 20
The phrase [I]is[/I] means equal to, so we set h - 20 equal to 59
[B]h - 20 = 59[/B]

59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving.

59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving.
The phrase [I]the sum of[/I] means we add Donnie's savings of d to 16:
d + 16
The phrase [I]is[/I] means an equation, so we set d + 16 equal to 59
d + 16 = 59 <-- [B]This is our algebraic expression[/B]
Now, if the problem asks you to solve for d, then you[URL='https://www.mathcelebrity.com/1unk.php?num=d%2B16%3D59&pl=Solve'] type the algebraic expression into our search engine to get[/URL]:
d = [B]43[/B]

6 books cost 9.24. How much is 1 book

6 books cost 9.24. How much is 1 book
Set up a proportion of cost to books where x is the cost for 1 book:
9.24/6 = x/1
To solve this proportion for x, we [URL='https://www.mathcelebrity.com/prop.php?num1=9.24&num2=x&den1=6&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
x = [B]1.54[/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 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 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 is the sum of 22 and Helenas height. Use the variable h to represent Helenas height.

60 is the sum of 22 and Helenas height. Use the variable h to represent Helenas height.
If height is represented by h, we have: 22 and h
22 + h
When they say "is the sum of", we set 22 + h equal to 60
[B]22 + h = 60[/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]

63 is the sum of 24 and helenas age

Set up an equation where h is Helena's age.
h + 24 = 63
[URL='http://www.mathcelebrity.com/1unk.php?num=h%2B24%3D63&pl=Solve']Subtract 24 from each side[/URL]
h = 39

64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44.

64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44.
The phrase [I]difference between[/I] means we subtract 44 from a:
a - 44
The phrase [I]64 is[/I] means an equation, so we set a - 44 equal to 64
[B]a - 44 = 64 <-- This is our algebraic expression
[/B]
If you want to solve for a, then we [URL='https://www.mathcelebrity.com/1unk.php?num=a-44%3D64&pl=Solve']type this expression into our search engine[/URL] and get:
[B]a = 108[/B]

64 is 4 times the difference between Sarah’s age a, and 44.Assume Sarah is older than 44

64 is 4 times the difference between Sarah’s age a, and 44.Assume Sarah is older than 44
Difference between Sarah's age (a) and 44 (Assuming Sarah is older than 44):
a - 44
4 times the difference:
4(a - 44)
The word [I]is[/I] means equal to, so we set 4(a - 44) equal to 64 to get our algebraic expression:
[B]4(a - 44) = 64[/B]
If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=4%28a-44%29%3D64&pl=Solve']type this equation into our search engine[/URL] and we get:
a = [B]60[/B]

66 decreased by Janelle's savings is 15

66 decreased by Janelle's savings is 15
Let Janelle's savings be s.
66 decreased by s is:
66 - s
The word [I]is[/I] means equal so we set 66 - s equal to 15
[B]66 - s = 15[/B]

7 and 105 are successive terms in a geometric sequence. what is the term following 105?

7 and 105 are successive terms in a geometric sequence. what is the term following 105?
Geometric sequences are set up such that the next term in the sequence equals the prior term multiplied by a constant. Therefore, we express the relationship in the following equation:
7k = 105 where k is the constant
[URL='https://www.mathcelebrity.com/1unk.php?num=7k%3D105&pl=Solve']Type this equation into our search engine[/URL] and we get:
k = 15
The next term in the geometric sequence after 105 is found as follows:
105*15 = [B]1,575[/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

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 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 quotient of 12 and x is 2

7 plus the quotient of 12 and x is 2
The quotient of 12 and x:
12/x
7 plus the quotient of 12 and x:
7 + 12/x
The word [I]is[/I] means equal to, so we set 7 + 12/x equal to 2:
[B]7 + 12/x = 2[/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 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

76 subtracted from p is equal to the total of g and 227

76 subtracted from p is equal to the total of g and 227
We've got two algebraic expressions. Take them in pieces:
Part 1:
76 subtracted from p
We subtract 76 from the variable p
p - 76
Part 2:
The total of g and 227
The total means a sum, so we add 227 to g
g + 227
Now the last piece, the phrase [I]is equal to[/I] means an equation. So we set both algebraic expressions equal to each other:
[B]p - 76 = g + 227[/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 bricklayers can build a wall in 10 days. How long would it take 5 bricklayers to build?

8 bricklayers can build a wall in 10 days. How long would it take 5 bricklayers to build?
Set up a proportion of bricklayers to building time where t is the amount of time it takes 5 bricklayers to build a wall:
8/10 = 5/t
To solve this proportion for t, we [URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=5&den1=10&den2=t&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
t = [B]6.25 days[/B]

8 more than the product of x and 2 equals 4

8 more than the product of x and 2 equals 4
The product of x and 2:
2x
8 more than this, means we add 8:
2x + 8
Set this equal to 4:
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B8%3D4&pl=Solve']2x + 8 = 4[/URL] <-- Algebraic expression
to solve for x, type this into the search engine and we get [B]x = -2[/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]

9 divided by the sum of x and 4 is equal to 6 divided by x minus 4

9 divided by the sum of x and 4 is equal to 6 divided by x minus 4.
Build our two algebraic expressions first:
9 divided by the sum of x and 4
9/(x + 4)
6 divided by x minus 4
6/(x - 4)
The phrase [I]is equal to[/I] means and equation, so we set the algebraic expressions equal to each other:
[B]9/(x + 4) = 6/(x - 4) <-- This is our algebraic expression[/B]
[B][/B]
If the problem asks you to solve for x, we cross multiply:
9(x - 4) = 6(x + 4)
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%28x-4%29%3D6%28x%2B4%29&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]20[/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 is the sum of thrice x and y

9 is the sum of thrice x and y
Thrice x means multiply x by 3:
3x
Sum of this and y:
3x + y
Now we set this expression equal to 9:
[B]3x + y = 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 less than twice x is twice y

9 less than twice x is twice y
Twice x means we multiply x by 2:
2x
9 less than Twice x means we subtract 9 from 2x
2x - 9
Twice y means we multiply y by 2:
2y
The word [I]is[/I] means equal to, so we set 2x - 9 equal to 2y:
[B]2x - 9 = 2y[/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 times x is twice the sum of x and 5

9 times x is twice the sum of x and 5
9 times x:
9x
the sum of x and 5
x + 5
twice the sum of x and 5
2(x + 5)
The phrase [I]is[/I] means equal to, so we set 9x equal to 2(x + 5)
[B]9x = 2(x + 5)[/B]

963 animals on a farm, 159 sheep and 406 cows and pigs. How many are pigs?

963 animals on a farm, 159 sheep and 406 cows and pigs. How many are pigs?
Set up equation to represent the total animals on the farm
Total Animals = Cows + Pigs + Sheep
Now plug in what is given
963 = 406 + Pigs + 159
Simplify:
Pigs + 565 = 963
Subtract 565 from each side
[B]Pigs = 398[/B]

A 1.5 inch tall preying mantis will sometimes hold its ground and attempt to fight a person who is 6

A 1.5 inch tall preying mantis will sometimes hold its ground and attempt to fight a person who is 6 feet tall. If a person who is 6 feet tall is engaged in a battle with an animal that was proportionally as tall as the person is to the preying mantis, how tall would the animal be?
In terms of inches, [URL='https://www.mathcelebrity.com/linearcon.php?quant=6&pl=Calculate&type=foot']6 feet = 72 inches[/URL]
Set up a proportion of height of smaller creature to larger creature where h is the heigh of the animal
1.5/72 = 72/h
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=1.5&num2=72&den1=72&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
h = 3456 inches
In terms of feet, we have [URL='https://www.mathcelebrity.com/linearcon.php?quant=3456&pl=Calculate&type=inch']3456 inches[/URL] = [B]288 feet[/B]

A 10 ounce serving of energy drink contains about 190 mg of caffeine approximately how much caffeine

A 10 ounce serving of energy drink contains about 190 mg of caffeine approximately how much caffeine is in a 25 ounce of energy drink?
Set up a proportion of caffeine to ounces where c is the amount of caffeine in a 25 ounce drink:
190/10 = c/25
[URL='https://www.mathcelebrity.com/prop.php?num1=190&num2=c&den1=10&den2=25&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL] and we get:
c = [B]475[/B]

A 12% acid solution is made by mixing 8% and 20% solutions. If the 450 ml of the 12% solution is req

A 12% acid solution is made by mixing 8% and 20% solutions. If the 450 ml of the 12% solution is required, how much of each solution is required?
Component Unit Amount
8% Solution: 0.08 * x = 0.08x
20% Solution: 0.2 * y = 0.2y
12% Solution: 0.12 * 450 = 54
We add up the 8% solution and 20% solution to get two equations:
[LIST=1]
[*]0.08x + 0.2y = 54
[*]x + y = 450
[/LIST]
We have a simultaneous set of equations. We can solve it using three methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]x = 300 ml[/B]
[*][B]y = 150 ml[/B]
[/LIST]

A 12-ounce bottle of shampoo lasts Enrique 16 weeks. How long would you expect an 18-ounce bottle of

A 12-ounce bottle of shampoo lasts Enrique 16 weeks. How long would you expect an 18-ounce bottle of the same brand to last him?
Set up a proportion of ounces to weeks were w is the amount of weeks an 18-ounce bottle will last:
12/16 = 18/w
We [URL='https://www.mathcelebrity.com/prop.php?num1=12&num2=18&den1=16&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion in our search engine to solve for w[/URL] and we get:
w = [B]24[/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

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 want a {1, 2, 3, 4, 5}
P(X < 6) =[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 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an ho

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey?
[U]Set up the relationship of still water speed and downstream speed[/U]
Speed down stream = Speed in still water + speed of the current
Speed down stream = x+2
Therefore:
Speed upstream =x - 2
Since distance = rate * time, we rearrange to get time = Distance/rate:
15/(x+ 2) + 15 /(x- 2) = 3
Multiply each side by 1/3 and we get:
5/(x + 2) + 5/(x - 2) = 1
Using a common denominator of (x + 2)(x - 2), we get:
5(x - 2)/(x + 2)(x - 2) + 5(x + 2)/(x + 2)(x - 2)
(5x - 10 + 5x + 10)/5(x - 2)/(x + 2)(x - 2)
10x = (x+2)(x-2)
We multiply through on the right side to get:
10x = x^2 - 4
Subtract 10x from each side:
x^2 - 10x - 4 = 0
This is a quadratic equation. To solve it, [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2-10x-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine[/URL] and we get:
Speed of the boat in still water =X=5 +- sq. Root of 29 kmph
We only want the positive solution:
x = 5 + sqrt(29)
x = 10.38
[U]Calculate time for upstream journey:[/U]
Time for upstream journey = 15/(10.38 - 2)
Time for upstream journey = 15/(8.38)
Time for upstream journey = [B]1.79[/B]
[U]Calculate time for downstream journey:[/U]
Time for downstream journey = 15/(10.38 + 2)
Time for downstream journey = 15/(12.38)
Time for downstream journey = [B]1.21[/B]

A 3-foot stick casts a shadow of 8 feet. If at the same time a tree casts a shadow of 15 feet, how t

A 3-foot stick casts a shadow of 8 feet. If at the same time a tree casts a shadow of 15 feet, how tall is the tree?
Set up a proportion of height to shadow length where t is the height of a tree:
3/8 = t/15
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3&num2=t&den1=8&den2=15&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
t = [B]5.625[/B]

A = {1, 3, 5, 7, 9} B = {2, 4, 6, 8, 10} C = {1, 5, 6, 7, 9} A ? (B ? C) =

A = {1, 3, 5, 7, 9} B = {2, 4, 6, 8, 10} C = {1, 5, 6, 7, 9} A ? (B ? C) =
B ? C = {6}
A ? (B ? C) = [B]{} or the empty set[/B]

A bag of rice says to mix 3 cups of rice with 2 cups of water. How much water would be needed to mix

A bag of rice says to mix 3 cups of rice with 2 cups of water. How much water would be needed to mix with 2 cups of rice?
Set up a proportion of cups of rice to water where w is the amount of water needed for 2 cups of rice:
3/2 = 2/w
To solve this proportion for w, we [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=2&den1=2&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
w = [B]1.33333[/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 offers a sale price of $3.50 for 4 muffins. What is the price per dozen?

A bakery offers a sale price of $3.50 for 4 muffins. What is the price per dozen?
1 dozen = 12 muffins
What this problem is really asking, $3.50 for 4 muffins. Let p be the price for 12 muffins (1 dozen). Set up a proportion of cost to muffins.
3.50/4 = p/12
Using our math engine, we [URL='https://www.mathcelebrity.com/prop.php?num1=3.50&num2=p&den1=4&den2=12&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search box[/URL] and get:
p = [B]10.5 muffins
[MEDIA=youtube]ccY7yDkKvzs[/MEDIA][/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 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 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 bedroom set that normally sells for $1100 is on sale for 15% off. If sales tax rate is 2%, what is

A bedroom set that normally sells for $1100 is on sale for 15% off. If sales tax rate is 2%, what is the total price of the bedroom set if it is bought while on sale?
[U]Calculate the sale price:[/U]
Sale Price = Normal Price * (1 - Sales Percentage)
[U]With our sales percentage of 15% = 0.15, we have:[/U]
Sale Price = 1100 * (1 - 0.15)
Sale Price = 1100 * (0.85)
Sale Price = 935
[U]Calculate post tax amount:[/U]
Post tax amount = Sale Price * (1 + Tax Percentage)
[U]With our tax percentage of 2% = 0.02, we have:[/U]
Post tax amount = 935 * (1 + 0.02)
Post tax amount = 935 * (1.02)
Post tax amount = [B]$953.70[/B]

A belongs to Both X and Y

A belongs to Both X and Y
What this means is Element A belongs to Set X and Set Y.
We write this as follows
A is an element of X is written as A ? X
A is an element of Y is written as A ? Y
[B]A ? X & A ? Y[/B]
[FONT=Droid Serif][COLOR=rgb(34, 34, 34)][SIZE=14px][/SIZE][/COLOR][/FONT]

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 brand new car that is originally valued at $25,000 depreciates by 8% per year. What is the value o

A brand new car that is originally valued at $25,000 depreciates by 8% per year. What is the value of the car after 6 years?
The Book Value depreciates 8% per year. We set up a depreciation equation:
BV(t) = BV(0) * (1 - 0.08)^t
The Book Value at time 0 BV(0) = 25,000. We want the book value at time 6.
BV(6) = 25,000 * (1 - 0.08)^6
BV(6) = 25,000 * 0.92^6
BV(6) = 25,000 * 0.606355
BV(6) = [B]15,158.88[/B]

A broken clock that loses 12 minutes every hour is set at 12:00 noon at the same time a normal clock

A broken clock that loses 12 minutes every hour is set at 12:00 noon at the same time a normal clock has its time set to 12:00 noon. When the broken clock reaches 12:00 midnight, what will the normal clock read?
Set up a proportion normal clock to broken clock:
60/48 = n/12
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=60&num2=n&den1=48&den2=12&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
n = [B]15 hours
[/B]
12:00 AM plus 15 hours = [B]3 pm[/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 $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 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 traveling on a freeway at 50 mph with the cruise control set at 50 mph. Another car is trav

A car is traveling on a freeway at 50 mph with the cruise control set at 50 mph. Another car is traveling at 90 mph with the cruise control set at 90 mph. Which car has a higher acceleration?
Acceleration means a change in speed.
Neither car has a change in speed, [B]so both cars have the same acceleration which is 0[/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 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 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 costs $20 for 400 minutes and $2 for each extra minute. Gina uses 408 minutes. How m

A cell phone costs $20 for 400 minutes and $2 for each extra minute. Gina uses 408 minutes. How much will it cost?
Set up the cost function for minutes (m) if m is greater than or equal to 400
C(m) = 20 + 2(m - 400)
For m = 408, we have:
C(408) = 20 + 2(408 - 400)
C(408) = 20 + 2(8)
C(408) = [B]36[/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 culture of the bacterium Streptococcus A initially has 8 bacteria and is observed to doubl

A certain culture of the bacterium Streptococcus A initially has 8 bacteria and is observed to double every 1.5 hours.After how many hours will the bacteria count reach 10,000.
Set up the doubling times:
0 | 8
1.5 | 16
3 | 32
4.5 | 64
6 | 128
7.5 | 256
9 | 512
10.5 | 1024
12 | 2048
13.5 | 4096
15 | 8192
16.5 | 16384
So at time [B]16.5[/B], we cross 10,000 bacteria.

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 city has a population of 240,000 people. Suppose that each year the population grows by 8%. What w

A city has a population of 240,000 people. Suppose that each year the population grows by 8%. What will the population be after 5 years?
[U]Set up our population function[/U]
P(t) = 240,000(1 + t)^n where t is population growth rate percent and n is the time in years
[U]Evaluate at t = 0.08 and n = 5[/U]
P(5) = 240,000(1 + 0.08)^5
P(5) = 240,000(1.08)^5
P(5) = 240,000 * 1.4693280768
[B]P(5) = 352638.73 ~ 352,639[/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 classroom had x students. Then 9 of them went home. There are now 27 students in the classroom.

A classroom had x students. Then 9 of them went home. There are now 27 students in the classroom.
Take this one piece at a time:
[LIST]
[*]We start with x students
[*]9 of them went home. This means we have 9 less students. So we subtract 9 from x: x - 9
[*]The phrase [I]there are now[/I] means an equation, so we set x - 9 equal to 27
[/LIST]
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 search engine[/URL] and we get:
x = [B]36[/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 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 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 is planning to manufacture a certain product. The fixed costs will be $474778 and it will

A company is planning to manufacture a certain product. The fixed costs will be $474778 and it will cost $293 to produce each product. Each will be sold for $820. Find a linear function for the profit, P , in terms of units sold, x .
[U]Set up the cost function C(x):[/U]
C(x) = Cost per product * x + Fixed Costs
C(x) = 293x + 474778
[U]Set up the Revenue function R(x):[/U]
R(x) = Sale Price * x
R(x) = 820x
[U]Set up the Profit Function P(x):[/U]
P(x) = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = 820x - (293x + 474778)
P(x) = 820x - 293x - 474778
[B]P(x) = 527x - 474778[/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 that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each l

A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each lamp, and the selling price is $150 per lamp.
Set up the Cost Equation C(l) where l is the price of each lamp:
C(l) = Variable Cost x l + Fixed Cost
C(l) = 90l + 1800
Determine the revenue function R(l)
R(l) = 150l
Determine the profit function P(l)
Profit = Revenue - Cost
P(l) = 150l - (90l + 1800)
P(l) = 150l - 90l - 1800
[B]P(l) = 60l - 1800[/B]
Determine the break even point:
Breakeven --> R(l) = C(l)
150l = 90l + 1800
[URL='https://www.mathcelebrity.com/1unk.php?num=150l%3D90l%2B1800&pl=Solve']Type this into the search engine[/URL], and we get [B]l = 30[/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 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 direct variation includes the points ( – 5, – 20) and (n,8). Find n.

A direct variation includes the points ( – 5, – 20) and (n,8). Find n.
Slopes are proportional for rise over run. Set up a proportion of x's to y's:
-5/n = -20/8
To solve this proportion for n, we [URL='https://www.mathcelebrity.com/prop.php?num1=-5&num2=-20&den1=n&den2=8&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
n = [B]2[/B]

A dog and a cat together cost $100. If the price of the dogs $90 more than the cat, what is the cost

A dog and a cat together cost $100. If the price of the dogs $90 more than the cat, what is the cost of the cat?
Set up givens and equations
[LIST]
[*]Let the cost of the dog be d
[*]Let the cost of the cat be c
[/LIST]
We're given 2 equations:
[LIST=1]
[*]c + d = 100
[*]d = c + 90
[/LIST]
Substitute equation (2) into equation (1) for d
c + c + 90 = 100
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=c%2Bc%2B90%3D100&pl=Solve']math engine[/URL], we see that:
c = [B]5
[/B]
Substitute c = 5 into equation (2) above:
d = 5 + 90
d = [B]95[/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 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 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 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 flea is very small, but can jump very high. For example, a flea that is 1/8 inch tall can jump 12

A flea is very small, but can jump very high. For example, a flea that is 1/8 inch tall can jump 12 inches in height. If a child who is 4 feet tall had the ability to jump like a flea, how high could she jump?
Set up a proportion of height to jump height where j is the jump height of the child:
1/8/12 = 4/j
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=0.125&num2=4&den1=12&den2=j&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
j = [B]384 feet[/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 grocer is selling oranges at 3 for $2. How much would it cost to buy a dozen oranges?

A grocer is selling oranges at 3 for $2. How much would it cost to buy a dozen oranges?
Set up a proportion of oranges per cost where c is the cost of a dozen oranges:
3/2 = 12/c <-- A dozen equals 12
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=12&den1=2&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
c = [B]8[/B]

A group of 4 adults and 5 children is visiting an amusement park. Admission is $15 per adult and $9

A group of 4 adults and 5 children is visiting an amusement park. Admission is $15 per adult and $9 per child. Find the total cost of admission for the group.
Set up the cost function for adults and children:
C(a, c) = 15a + 9c
We want the cost for 4 adults and 5 children
C(4, 5) = 15(4) + 9(5)
C(4, 5) = 60 + 45
C(4, 5) = [B]105[/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 home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 2

A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 20 feet less than 3 times the width, what are the dimensions of the rectangular plot?
[U]Set up equations:[/U]
(1) 2l + 2w = 800
(2) l = 3w - 20
[U]Substitute (2) into (1)[/U]
2(3w - 20) + 2w = 800
6w - 40 + 2w = 800
[U]Group the w terms[/U]
8w - 40 = 800
[U]Add 40 to each side[/U]
8w = 840
[U]Divide each side by 8[/U]
[B]w = 105
[/B]
[U]Substitute w = 105 into (2)[/U]
l = 3(105) - 20
l = 315 - 20
[B]l = 295[/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 is the set of factors of 12

A is the set of factors of 12
Type in [URL='https://www.mathcelebrity.com/factoriz.php?num=12&pl=Show+Factorization']factor 12[/URL] into our math engine and we get:
A = {[B]1, 2, 3, 4, 6, 12[/B]}

A is the set of integers greater than or equal to -5 and less than or equal to -2

A is the set of integers greater than or equal to -5 and less than or equal to -2
[B]-5 <= A <= -2[/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 ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall,

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall, how high up the wall does the ladder reach?
We have a right triangle, where the ladder is the hypotenuse, and we want the measurement of one leg.
Set up the pythagorean theorem with these given items using our P[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=7&hypinput=25&pl=Solve+Missing+Side']ythagorean Theorem Calculator[/URL].
We get Side 1 = [B]24 feet.[/B]

A line has a slope of 7 and a y-intercept of -4. What is its equation in slope intercept form

A line has a slope of 7 and a y-intercept of -4. What is its equation in slope intercept form
The slope-intercept equation for a line:
y = mx + b where m is the slope
Given m = 7, we have:
y = 7x + b
The y-intercept is found by setting x to 0:
y = 7(0) + b
y = 0 + b
y = b
We're given the y-intercept is -4, so we have:
b = -4
So our slope-intercept equation is:
[B]y = 7x - 4[/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 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 offers 1 $1000 prize and 5 $100 prizes. 1000 tickets are sold. Find the expectation if a p

A lottery offers 1 $1000 prize and 5 $100 prizes. 1000 tickets are sold. Find the expectation if a person buys 1 ticket for $5.
Set up the expected values E(x):
for the 1,000 price:
E(x) = (1000 - 5) * 1/1000 = 995/1000
For the 5 $100 prizes:
E(x) = (100 - 5) * 5/1000 = 475/1000
For the losing ticket. With 6 winning tickets, we have 1000 - 6 = 994 losing tickets:
E(x) = -3 * 994/1000 = -2982/1000
We get our total expected value by adding all of these expected values up. Since they all have the same denominator, we add numerators:
E(x) = (995 + 475 - 2982)/1000
E(x) = -1512/1000
E(x) = [B]-1.51[/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's age (a) 10 years ago is 43

A man's age (a) 10 years ago is 43
[U]10 years ago means we subtract 10 from a:[/U]
a - 10
[U]The word [I]is[/I] means an equation. So we set a - 10 equal to 43 to get our algebraic expression[/U]
[B]a - 10 = 43[/B]
If the problem asks you to solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=a-10%3D43&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = 53

A manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produce

A manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produced. The product sells for $10/unit.
Set up cost function where u equals each unit produced:
C(u) = 7u + 25,500
Set up revenue function
R(u) = 10u
Break Even is where Cost equals Revenue
7u + 25,500 = 10u
Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=7u%2B25500%3D10u&pl=Solve']equation calculator[/URL] to get [B]u = 8,500[/B]

a manufacturing company has a debt to equity ratio of 3 to 2. if the company has a debt of $12 milli

a manufacturing company has a debt to equity ratio of 3 to 2. if the company has a debt of $12 million, how much does it have in equity?
Set up a proportion of debt to equity
3/2 = 12/x
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=3&num2=12&den1=2&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
x = 8

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 medium orange has 70 calories. This is 10 calories less then 1/4 of the calories in a sugar krunch

A medium orange has 70 calories. This is 10 calories less then 1/4 of the calories in a sugar krunchy. How many calories are in a sugar crunchy?
Let s = calories in a sugar crunch. Let o = 70 be the calories in a medium orange. Set up the equation:
o = 1/4s - 10
70 = 1/4s - 10
Add 10 to each side
1/4s = 80
Multiply each side by 4
[B]s = 320[/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 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 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 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 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 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 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 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 pack of 36 black sharp tip markers costs $34.49. What is the price of one marker?

A pack of 36 black sharp tip markers costs $34.49. What is the price of one marker?
Set up unit cost:
34.49/36 = [B]$0.96 per marker[/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 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 who had $1,000,000 gave $100 to charity. How much must a student who has $100 give to chari

A person who had $1,000,000 gave $100 to charity. How much must a student who has $100 give to charity to give proportionally the same as the millionaire?
Set up a proportion of wealth owned to donation where x is the amount the student gives:
1000000/100 = 100/x
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=1000000&num2=100&den1=100&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
[B]x = 0.01[/B]

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the custome

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 8 cents per minute of use. In Plan B, the customer pays a monthly fee of $1.50 and then an additional 7 cents per minute of use.
For what amounts of monthly phone use will Plan A cost more than Plan B?
Set up the cost equations for each plan. The cost equation for the phone plans is as follows:
Cost = Cost Per Minute * Minutes + Monthly Fee
Calculate the cost of Plan A:
Cost for A = 0.08m + 0. <-- Since there's no monthly fee
Calculate the cost of Plan B:
Cost for B = 0.07m + 1.50
The problem asks for what amounts of monthly phone use will Plan A be more than Plan B. So we set up an inequality:
0.08m > 0.07m + 1.50
[URL='https://www.mathcelebrity.com/1unk.php?num=0.08m%3E0.07m%2B1.50&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]m > 150
This means Plan A costs more when you use more than 150 minutes per month.[/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 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 plane is flying at an altitude of 45,000 feet. It begins to drop in altitude 3,000 feet per minute

A plane is flying at an altitude of 45,000 feet. It begins to drop in altitude 3,000 feet per minute. What is the slope in this situation?
Set up a graph where minutes is on the x-axis and altitude is on the y-axis.
[LIST=1]
[*]Minute 1 = (1, 42,000)
[*]Minute 2 = (2, 39,000)
[*]Minute 3 = (3, 36,000)
[*]Minute 4 = (4, 33,000)
[/LIST]
You can see for every 1 unit move in x, we get a -3,000 unit move in y.
Pick any of these 2 points, and [URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=42000&slope=+2%2F5&xtwo=2&ytwo=39000&bvalue=+&pl=You+entered+2+points']use our slope calculator[/URL] to get:
Slope = -[B]3,000[/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 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 charges $50 to visit a house plus $40 for every hour of work.

A plumber charges $50 to visit a house plus $40 for every hour of work.
Set up the cost function in terms of hours (h) using the flat fee of $50
[B]C(h) = 40h + 50[/B]

A police officer is trying to catch a fleeing criminal. The criminal is 20 feet away from the cop, r

A police officer is trying to catch a fleeing criminal. The criminal is 20 feet away from the cop, running at a rate of 5 feet per second. The cop is running at a rate of 6.5 feet per second. How many seconds will it take for the police officer to catch the criminal?
Distance = Rate * Time
[U]Criminal:[/U]
5t + 20
[U]Cop[/U]:
6.5t
We want to know when their distances are the same (cop catches criminal). So we set the equations equal to each other:
5t + 20 = 6.5t
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=5t%2B20%3D6.5t&pl=Solve']we type it in our search engine[/URL] and we get:
t = 13.333 seconds

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 printer charges a $30 setup fee plus $2.00 per ticket. Write an algebraic expression for the cost

a printer charges a $30 setup fee plus $2.00 per ticket. Write an algebraic expression for the cost of t tickets. What is the cost of 225 tickets?
Algebraic Expression:
Cost per ticket * t + set up fee
[B]2t + 30[/B]
How much for t = 225?
2(225) + 30
450 + 30
[B]480[/B]

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 random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afte

A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes).
Checkout Time (in minutes) | Frequency | Relative Frequency
1.0 - 1.9 | 2 | ?
2.0 - 2.9 | 8 | ?
3.0 - 3.9 | ? | ?
4.0 - 5.9 | 5 | ?
Total | 25 | ?
(a) Complete the frequency table with frequency and relative frequency.
(b) What percentage of the checkout times was less than 3 minutes?
(c)In what class interval must the median lie? Explain your answer.
(d) Assume that the largest observation in this dataset is 5.8. Suppose this observation were incorrectly recorded as 8.5 instead of 5.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Why?
(a)
[B]Checkout Time (in minutes) | Frequency | Relative Frequency
1.0 - 1.9 | 2 | 2/25
2.0 - 2.9 | 8 | 8/25
3.0 - 3.9 | 10 (since 25 - 5 + 8 + 2) = 10 | 10/25
4.0 - 5.9 | 5 | 5/25
Total | 25 | ?[/B]
(b) (2 + 8)/25 = 10/25 = [B]40%[/B]
c) [B]3.0 - 3.9[/B] since 2 + 8 + 10 + 5 = 25 and 13 is the middle value which occurs in the 3.0 - 3.9 interval
(d) [B]Mean increases[/B] since it's a higher value than usual. Median would not change as the median is the most frequent distribution and assuming the 5.8 is only recorded once.

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 recipe of 20 bread rolls requires 5 tablespoons of butter. How many tablespoons of butter are need

a recipe of 20 bread rolls requires 5 tablespoons of butter. How many tablespoons of butter are needed for 30 bread rolls?
Set up a proportion of bread rolls per tablespoons of butter where t is the amount of tablespoons of butter needed for 30 bread rolls:
20/5 = 30/t
Cross multiply our proportion:
Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2
20t = 30 * 5
20t = 150
Divide each side of the equation by 20:
20t/20 = 150/20
Cancel the 20's on the left side and we get:
t = [B]7.5[/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 rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find i

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find its length and width.
The area of a rectangle (A) is:
A = lw --> where l is the length and w is the width
We're given l = 2w, so we substitute this into the Area equation:
A = (2w)w
A = 2w^2
We're given the area of the pitch is 360, so we set:
2w^2 = 360
We [URL='https://www.mathcelebrity.com/1unk.php?num=2w%5E2%3D360&pl=Solve']type this equation into our search engine[/URL], follow the links, and get:
w = [B]6*sqrt(5)
[/B]
Now we take this, and substitute it into this equation:
6*sqrt(5)l = 360
Dividing each side by 6*sqrt(5), we get:
l = [B]60/sqrt(5)[/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 revenue function is R(x) = 22x and a cost function is C(x) = -9x + 341. The break-even point is

A revenue function is R(x) = 22x and a cost function is C(x) = -9x + 341. The break-even point is
Break even is when C(x) = R(x). So we set them equal and solve for x:
-9x + 341 = 22x
Typing[URL='https://www.mathcelebrity.com/1unk.php?num=-9x%2B341%3D22x&pl=Solve'] this equation into our search engine[/URL], we get:
x = [B]11[/B]

a rocket is propelled into the air. its path can be modelled by the relation h = -5t^2 + 50t + 55, w

a rocket is propelled into the air. its path can be modeled by the relation h = -5t^2 + 50t + 55, where t is the time in seconds, and h is height in metres. when does the rocket hit the ground
We set h = 0:
-5t^2 + 50t + 55 = 0
Typing this quadratic equation into our search engine to solve for t, we get:
t = {-1, 11}
Time can't be negative, so we have:
t = [B]11[/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 salesperson works 40 hours per week at a job where he has two options for being paid. Option A is

A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $24. Option B is a commission rate of 4% on weekly sales. How much does he need to sell this week to earn the same amount with the two options?
Option A payment function:
24h
With a 40 hour week, we have:
24 * 40 = 960
Option B payment function with sales amount (s):
0.04s
We want to know the amount of sales (s) where Option A at 40 hours = Option B. So we set both equal to each other:
0.04s = 960
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.04s%3D960&pl=Solve']type it in our math engine[/URL] and we get:
s = [B]24,000[/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 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 has a cardinality of 9. How many proper subsets does the set have?

A set has a cardinality of 9. How many proper subsets does the set have?
The set has 2^9 = [B]512 proper subsets[/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 set of 4 consecutive integers adds up to 314. What is the least of the 4 integers?

A set of 4 consecutive integers adds up to 314. What is the least of the 4 integers?
First integer is x. The next 3 are x + 1, x + 2, and x + 3. Set up our equation:
x + (x + 1) + (x + 2) + (x + 3) = 314
Group x terms and group constnats
(x + x + x + x) + (1 + 2 + 3) = 314
Simplify and combine
4x + 6 = 314
[URL='http://www.mathcelebrity.com/1unk.php?num=4x%2B6%3D314&pl=Solve']Enter this in the equation solver[/URL]
[B]x = 77[/B]

A set of 6 wooden chairs costs $444. A set of 8 metal chairs costs $720. How much more do the metal

A set of 6 wooden chairs costs $444. A set of 8 metal chairs costs $720. How much more do the metal chairs cost per chair?
[U]Wooden Chair Unit Cost:[/U]
Unit Cost = Total Cost / Quantity
Unit Cost = 444/6
Unit Cost = 74
[B][/B]
[U]Metal Chair Unit Cost:[/U]
Unit Cost = Total Cost / Quantity
Unit Cost = 720/8
Unit Cost = 90
[B][B][/B][/B]
Find the difference (how much more)
Difference = Metal Chair Unit Cost - Wooden Chair Unit Cost
Difference = 90 - 74
Difference = [B]16[/B]

A set of data has a range of 30. The least value in the set of data is 22. What is the greatest valu

A set of data has a range of 30. The least value in the set of data is 22. What is the greatest value in the set of data?
High Value - Low Value = Range
Let the high value be h. We're given:
h - 22 = 30
We [URL='https://www.mathcelebrity.com/1unk.php?num=h-22%3D30&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]52[/B]

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 shopper paid $51.93 including tax for an item marked $48.99. What would she pay for another item m

A shopper paid $51.93 including tax for an item marked $48.99. What would she pay for another item marked $75?
Set up a proportion, assuming identical tax rates:
51.93/48.99 = 75/x where x is the after-tax amount
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=51.93&num2=75&den1=48.99&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
[B]x = 70.75[/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 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 stick that is ten feet tall casts a shadow of 12 feet. If a tree has a 96 foot shadow, how tall is

A stick that is ten feet tall casts a shadow of 12 feet. If a tree has a 96 foot shadow, how tall is the tree?
Set up a proportion of wood height to shadow length where h is the height of the tree:
10/12 = h/96
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=10&num2=h&den1=12&den2=96&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
h = [B]80 feet[/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 owner bought 240 cartons of eggs. The owner sold 5/8 of the eggs and set aside 5 cartons. Ho

A store owner bought 240 cartons of eggs. The owner sold 5/8 of the eggs and set aside 5 cartons. How many cartons of eggs did the owner have left to sale?
If the owner sold 5/8 of the eggs, they have 1 - 5/8 left.
1 = 8/8, so we have 8/8 - 5/8 = 3/8 left
3/8 (240 cartons) = 90 cartons remaining
The owner set aside 5 cartons.
We're left with 90 cartons - 5 cartons = [B]85 cartons[/B]

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 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 sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a.

A sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a. 40 years b. 50 years c. 30 years d. 60 years e. 80 years
Simple interest formula if we start with 1 dollar and double to 2 dollars:
1(1 + i(20)) = 2
1 + 20i = 2
Subtract 1 from each side:
20i = 1
Divide each side by 20
i = 0.05
Now setup the same simple interest equation, but instead of 2, we use 3:
1(1 + 0.05(t)) = 3
1 + 0.05t = 3
Subtract 1 from each side:
0.05t = 2
Divide each side by 0.05
[B]t = 40 years[/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 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 test has twenty questions worth 100 points . The test consist of true/false questions worth 3 poin

A test has twenty questions worth 100 points . The test consist 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?
Set up equations where t = true false and m = multiple choice:
[LIST=1]
[*]t + m = 20
[*]3t + 11m = 100
[/LIST]
Use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=t+%2B+m+%3D+20&term2=3t+%2B+11m+%3D+100&pl=Cramers+Method']simultaneous equation calculator[/URL]:
[B]t = 15, m = 5[/B]

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 total of one and x is less than 5

a total of one and x is less than 5
A total of one and x means we add x to 1:
1 + x
We set up an inequality, where 1 + x is less than (<) 5
[B]1 + x < 5[/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 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 leaves San Diego at 1:00 PM. A second train leaves the same city in the same direction at 3

A train leaves San Diego at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 30mph faster than the first. If the second train overtakes the first at 6:00 PM, what is the speed of each of the two trains?
Distance = Rate x Time
Train 1:
d = rt
t = 1:oo PM to 6:00 PM = 5 hours
So we have d = 5r
Train 2:
d = (r + 30)t
t = 3:oo PM to 6:00 PM = 3 hours
So we have d = 3(r + 30)
Set both distances equal to each other since overtake means Train 2 caught up with Train 1, meaning they both traveled the same distance:
5r = 3(r + 30)
Multiply through:
3r + 90 = 5r
[URL='https://www.mathcelebrity.com/1unk.php?num=3r%2B90%3D5r&pl=Solve']Run this equation through our search engine[/URL], and we get [B]r = 45[/B]. This is Train 1's Speed.
Train 2's speed = 3(r + 30).
Plugging r = 45 into this, we get 3(45 + 30).
3(75)
[B]225[/B]

A trapezoid has one base that is 120% of the length of the other base. The two sides are each 1/2 th

A trapezoid has one base that is 120% of the length of the other base. The two sides are each 1/2 the length of the smaller base. If the perimeter of the trapezoid is 54.4 inches, what is the length of the smaller base of the trapezoid?
Setup measurements:
[LIST]
[*]Small base = n
[*]Large base = 1.2n
[*]sides = n/2
[*]Perimeter = n + 1.2n + 0.5n + 0.5n = 54.4
[/LIST]
Solve for [I]n[/I] in the equation n + 1.2n + 0.5n + 0.5n = 54.4
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(1 + 1.2 + 0.5 + 0.5)n = 3.2n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
3.2n = + 54.4
[SIZE=5][B]Step 3: Divide each side of the equation by 3.2[/B][/SIZE]
3.2n/3.2 = 54.4/3.2
n = [B]17[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=n%2B1.2n%2B0.5n%2B0.5n%3D54.4&pl=Solve']Source[/URL]

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 typical human adult weighs 150 pounds, while a human newborn weighs approximately 7 pounds. An adu

A typical human adult weighs 150 pounds, while a human newborn weighs approximately 7 pounds. An adult female Western Grey Kangaroo weighs about 30 kilograms and gives birth to babies who are approximately one gram. If human babies were proportionally the same weight as adults as Western Grey Kangaroos babies, how much would a human newborn weigh?
Set up a proportion of adult weight to baby weight where n is the weight of a human baby:
30000/1 = 150/n
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=30000&num2=150&den1=1&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
n = [B]0.005 or 1/200 of a pound[/B]

A U ? = A

A U ? = A
Let x ? [I]S[/I], where [I]S[/I] is the universal set.
First we show that if A ? Ø ? A.
Let x ? A ? Ø.
Then x ? A or x ? Ø. by definition of the empty set, x cannot be an element in Ø.
So by assumption, x ? A ? Ø, x must be in A.
So A ? Ø ? A.
Next, we show that A ? A ? Ø.
This is true because the set resulting from the union of two sets contains both of the sets forms the union
Since A ? Ø ? A and A ? A ? Ø, we have that A ? Ø = A.

A vehicle purchased for $25,000 depreciates at a constant rate of 5%. Determine the approximate valu

A vehicle purchased for $25,000 depreciates at a constant rate of 5%. Determine the approximate value of the vehicle 11 years after purchase. Round to the nearest whole dollar.
Depreciation at 5% means it retains 95% of the value. Set up the depreciation equation to get Book Value B(t) at time t.
B(t) = $25,000 * (1 - 0.05)^t
Simplifying, this is:
B(t) = $25,000 * (0.95)^t
The problem asks for B(11)
B(11) = $25,000 * (0.95)^11
B(11) = $25,000 * 0.5688
B(11) = [B]$14,220[/B]

A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor

A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost?
Let the cost of the soda be p. So the cost of a hot dog is 2p.
The total cost of hot dogs:
2hp
The total cost of sodas:
ps
The total cost of both equals d. So we set the total cost of hots dogs plus sodas equal to d:
2hp + ps = d
We want to know the cost of a soda (p). So we have a literal equation. We factor out p from the left side:
p(2h + s) = d
Divide each side of the equation by (2h + s)
p(2h + s)/(2h + s) = d/(2h + s)
Cancel the (2h + s) on the left side, we get:
p = [B]d/(2h + s[/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 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 wildlife reserve has a population of 180 elephants. A group of researchers trapped 60 elephants an

A wildlife reserve has a population of 180 elephants. A group of researchers trapped 60 elephants and recorded their vital statistics. Of the trapped elephants, 12 were female. If that rate holds true for the entire population of 180 elephants, how many female elephants are on the wildlife reserve?
Set up a proportion of female to trapped elephants:
12/60 = f/180
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=12&num2=f&den1=60&den2=180&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we see that f = [B]36[/B]

A yardstick casts a shadow of 8 inches. At the same time, a tree casts a shadow of 52 feet. How tall

A yardstick casts a shadow of 8 inches. At the same time, a tree casts a shadow of 52 feet. How tall is the tree?
Setup a proportion of height to shadow distance where h is the height of the tree:
36/8 = h/52
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=36&num2=h&den1=8&den2=52&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
h = [B]234 feet[/B]

A yoga member ship costs $16 and additional $7 per class. Write a linear equation modeling the cost

A yoga member ship costs $16 and additional $7 per class. Write a linear equation modeling the cost of a yoga membership?
Set up the cost function M(c) for classes (c)
[B]M(c) = 16 + 7c[/B]

A young dad, who was a star football player in college, set up a miniature football field for his fi

A young dad, who was a star football player in college, set up a miniature football field for his five-year-old young daughter, who was already displaying an unusual talent for place-kicking. At each end of the mini-field, he set up goal posts so she could practice kicking extra points and field goals. He was very careful to ensure the goalposts were each straight up and down and that the crossbars were level. On each set, the crossbar was six feet long, and a string from the top of each goalpost to the midpoint between them on the ground measured five feet. How tall were the goalposts? How do you know this to be true?
The center of each crossbar is 3 feet from each goalpost. We get this by taking half of 6, since midpoint means halfway.
Imagine a third post midway between the two goal posts. It has the same height as the two goalposts.
From the center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=3&hypinput=5&pl=Solve+Missing+Side']Using the Pythagorean Theorem[/URL], the other leg -- the height of each post -- is 4 feet.

absolute value of x is less than or equal to 4

absolute value of x is less than or equal to 4
Absolute value of x:
|x|
Set up an inequality where this is less than or equal to 4:
[B]|x| <= 4 [/B] <-- This is our algebraic expression
To solve this, we have the following compound inequality:
-4 < x < 4

Absolute value of x less than 8

Absolute value of x is denoted as |x|.
Set that to less than 8, we have:
|x| < 8

Accounting Rate of Return

Given an initial investment and a set of returns, this calculates the Accounting Rate of Return

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]

Algebraic Substitutions

Given an algebraic statement with variables [a-z], this calculator takes a set of given substitution values, i.e., x=2,y=3,z=4, and evaluates your statement using the substitution values.

Alicia deposited $41 into her checking account. She wrote checks for $31 and $13. Now her account ha

Alicia deposited $41 into her checking account. She wrote checks for $31 and $13. Now her account has a balance of $81. How much did she have in her account to start with?
We start with a balance of b.
Depositing 41 means we add to the account balance:
b + 41
Writing checks for 31 and 13 means we subtract from the account balance:
b + 41 - 31 - 13
The final balance is 81, so we set b + 41 - 31 - 13 equal to 81:
b + 41 - 31 - 13 = 81
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B41-31-13%3D81&pl=Solve']type this equation into our math engine[/URL] and we get:
b = [B]84[/B]

All the colors of the rainbow

All the colors of the rainbow
You can find this with the acronym: ROYGBIV
[LIST=1]
[*][B]Red[/B]
[*][B]Orange[/B]
[*][B]Yellow[/B]
[*][B]Green[/B]
[*][B]Blue[/B]
[*][B]Indigo[/B]
[*][B]Violet[/B]
[/LIST]
[U]Written as a set, we have 7 elements:[/U]
{[B]Red, Orange, Yellow, Green, Blue, Indigo, Violet[/B]}

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]

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]

Amelia had n shoes in her closet. How many pair of shoes did she have?

Amelia had n shoes in her closet. How many pair of shoes did she have?
1 pair = 2 shoes, so we have:
n[B]/2[/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]

An alligators tail length, T, varies directly as its body length, B. An alligator with a body length

An alligators tail length, T, varies directly as its body length, B. An alligator with a body length of 5.6 feet has a tail length of 4.9 feet. What is the tail length of an alligator whos body length is 4.8 feet
Set up a proportion of T/B
5.6/4.9 = t/4.8
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=5.6&num2=t&den1=4.9&den2=4.8&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]t = 5.49[/B].

An ancient Greek was said to have lived 1/4 of his live as a boy, 1/5 as a youth, 1/3 as a man, and

An ancient Greek was said to have lived 1/4 of his live as a boy, 1/5 as a youth, 1/3 as a man, and spent the last 13 years as an old man. How old was he when he died?
Set up his life equation per time lived as a boy, youth, man, and old man
1/4 + 1/5 + 1/3 + x = 1.
Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=3&num3=5&pl=LCM']LCM Calculator[/URL], we see the LCM of 3,4,5 is 60. This is our common denominator.
So we have 15/60 + 12/60 + 20/60 + x/60 = 60/60
[U]Combine like terms[/U]
x + 47/60 = 60/60
[U]Subtract 47/60 from each side:[/U]
x/60 = 13/60
x = 13 out of the 60 possible years, so he was [B]60 when he died[/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 experienced accountant can balance the books twice as fast as a new accountant. Working together

An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 10 hours. How long would it take the experienced accountant working alone?
Person A: x/2 job per hour
Person B: 1/x job per hour
Set up our equation:
1/x + 1/(2x) = 1/10
Multiply the first fraction by 2/2 to get common denominators;
2/(2x) + 1/(2x) = 1/10
Combine like terms
3/2x = 1/10
Cross multiply:
30 = 2x
Divide each side by 2:
[B]x = 15[/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]

Analysis of Variance (ANOVA)

Performs 1 way analysis of variance or 2 way analysis of variance on a set of data with critical value test and conclusion.

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 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]

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]

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 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 the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on

At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on a movie and popcorn and another $1.35 on a pen. How much did she earn babysitting?
Let the original amount of money earned for babysitting be b. We're given:
[LIST=1]
[*]Start with b
[*]Spending 14.65 for a movie means we subtract 14.65 from b: b - 14.65
[*]Spending 1.35 on a pen means we subtract another 1.35 from step 2: b - 14.65 - 1.35
[*]Francesca has a third of her money left. So we set step 3 equal to 1/3 of b
[/LIST]
b - 14.65 - 1.35 = b/3
Multiply each side of the equation by 3 to remove the fraction
3(b - 14.65 - 1.35) = 3b/3
3b - 43.95 - 4.05 = b
To solve this equation for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b-43.95-4.05%3Db&pl=Solve']we type it in our search engine[/URL] and we get:
b =[B] 24[/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].

Ava set her watch 2 seconds behind, every day it sets back 1 second. How many days has it been since

Ava set her watch 2 seconds behind, every day it sets back 1 second. How many days has it been since she last set her watch if it is 41 seconds behind?
Right now: Watch is 2 seconds behind
[U]Let d be the day after right now[/U]
(1)d + 2 = 41
d + 2 = 41
[U]Subtract 2 from each side[/U]
[B]d = 39[/B]

average of 16 and x is three. find x

average of 16 and x is three. find x
Average of 16 and x is written as:
(16 + x)/2
We set this equal to 3:
(16 + x)/2 = 3
Cross multiply;
x + 16 = 6
[URL='https://www.mathcelebrity.com/1unk.php?num=x%2B16%3D6&pl=Solve']Type this equation into our search engine[/URL] and we get:
x = [B]-10[/B]

B is the set of vowels in the English alphabet

B is the set of vowels in the English alphabet
B = [B]{a, e, i, o, u}
[MEDIA=youtube]-O686SiqLrk[/MEDIA][/B]

B out of 6 is 12

B out of 6 is 12
b out of 6:
b/6
The phrase [I]is[/I] means an equation, so we set b/6 equal to 12:
[B]b/6 = 12[/B]

Balance Sheet

Given various asset and liability entries, this determines various calculations that can be made from the balance sheet.

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]

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]

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

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]

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 is 4 times as old as Ishaan and is also 6 years older than Ishaan.

Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan.
Let b be Ben's age and i be Ishaan's age. We're given:
[LIST=1]
[*]b = 4i
[*]b = i + 6
[/LIST]
Set (1) and (2) equal to each other:
4i = i + 6
[URL='https://www.mathcelebrity.com/1unk.php?num=4i%3Di%2B6&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]i = 2[/B]
Substitute this into equation (1):
b = 4(2)
[B]b = 8
[/B]
[I]Therefore, Ishaan is 2 years old and Ben is 8 years old.[/I]

Benfords Law

Shows you Benfords Law and evaluates a data set compared to Benfords Law

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].

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]

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]

Brandon can shovel his sidewalk in 8 minutes, while his brother can shovel the walk in 12 minutes. I

Brandon can shovel his sidewalk in 8 minutes, while his brother can shovel the walk in 12 minutes. If they work together, how long will it take them to shovel the sidewalk?
Set up unit rates:
[LIST]
[*]Brandon can shovel 1/8 of a sidewalk per minute
[*]His brother can shovel 1/12 of a sidewalk per minute
[/LIST]
Together, they can shovel:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F8&frac2=1%2F12&pl=Add']1/8 + 1/12[/URL] = 5/24 of a sidewalk per minute
1 minute = 60 seconds
5/24 / 60 seconds = 1/x seconds
5/24 * 60 = 1/x
5/1440 = 1/x
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5&num2=1&den1=1440&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
x = 288
288/60 = [B]4 minutes and 48 seconds[/B]

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

Caleb earns points on his credit card that he can use towards future purchases.

Let f = dollars spent on flights, h dollars spent on hotels, and p dollars spent on all other purchases.
[U]Set up our equations:[/U]
(1) 4f + 2h + p = 14660
(2) f + h + p = 9480
(3) f = 2h + 140
[U]First, substitute (3) into (2)[/U]
(2h + 140) + h + p = 9480
3h + p + 140 = 9480
3h + p = 9340
[U]Subtract 3h to isolate p to form equation (4)[/U]
(4) p = 9340 - 3h
[U]Take (3) and (4), and substitute into (1)[/U]
4(2h + 140) + 2h + (9340 - h) = 14660
[U]Multiply through[/U]
8h + 560 + 2h + 9340 - 3h = 14660
[U]Combine h terms and constants[/U]
(8 + 2 - 3)h + (560 + 9340) = 14660
7h + 9900 = 14660
[U]Subtract 9900 from both sides:[/U]
7h = 4760
[U]Divide each side by 7[/U]
[B]h = 680[/B]
[U]Substitute h = 680 into equation (3)[/U]
f = 2(680) + 140
f = 1360 + 140
[B]f = 1,500[/B]
[U]
Substitute h = 680 and f = 1500 into equation (2)[/U]
1500 + 680 + p = 9480
p + 2180 = 9480
[U]Subtract 2180 from each side:[/U]
[B]p = 7,300[/B]

Capitalized Cost and Periodic Charge

Given an Asset Value (A), a Salvage Value (S) at time (N), a sinking fund rate of (j), an effective rate of interest (i), and maintenance expense (M), this calculator solves for periodic charge (H) and capitalized cost (K)

Carlos age increased by is 16 is 62

Carlos age increased by is 16 is 62.
Let a be Carlos's age.
Increased by 16 means we add 16
a + 16
Now the phrase [I]is[/I] means equal to, so we set [B]a + 16 = 62[/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 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]

Cartesian Product

Given a Set A and Set B, this calculates the Cartesian Product A × B

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].

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]

Chinese Remainder Theorem

Given a set of modulo equations in the form:

x ≡ a mod b

x ≡ c mod d

x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.

Given that the n_{i} portions are not pairwise coprime and you entered two modulo equations, then the calculator will attempt to solve using the Method of Successive Subsitution

x ≡ a mod b

x ≡ c mod d

x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.

Given that the n

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse i

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse is 6 years older than Alex. The sum of their ages is 31 years. How old is each one of them?
Set up the relational equations where a = Alex's age, c = Chris's aged and j = Jesse's age
[LIST=1]
[*]a = c + 5
[*]j = a + 6
[*]a + c + j = 31
[*]Rearrange (1) in terms of c: c = a - 5
[/LIST]
[U]Plug in (4) and (2) into (3)[/U]
a + (a - 5) + (a + 6) = 31
[U]Combine like terms:[/U]
3a + 1 = 31
[U]Subtract 1 from each side[/U]
3a = 30
[U]Divide each side by 3[/U]
[B]a = 10[/B]
[U]Plug in 1 = 10 into Equation (4)[/U]
c = 10 - 5
[B]c = 5[/B]
Now plug 1 = 10 into equation (2)
j = 10 + 6
[B]j = 16[/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.

Class Frequency Goodness of Fit

Performs a goodness of fit test on a set of data with class boundaries (class boundary) with critical value test and conclusion.

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]

Combinations with Replacement

Calculates the following:

How many combinations can we have from a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed?

How many combinations can we have from a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed?

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]

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

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]

Consider the case of a manufacturer who has an automatic machine that produces an important part. Pa

Consider the case of a manufacturer who has an automatic machine that produces an important part. Past records indicate that at the beginning of the data the machine is set up correctly 70 percent of the time. Past experience also shows that if the machine is set up correctly it will produce good parts 90 percent of the time. If it is set up incorrectly, it will produce good parts 40 percent of the time. Since the machine will produce 60 percent bad parts, the manufacturer is considering using a testing procedure. If the machine is set up and produces a good part, what is the revised probability that it is set up correctly?
[U]Determine our events:[/U]
[LIST]
[*]C = Correctly Set Machine = 0.7
[*]C|G = Correctly Set Machine And Good Part = 0.9
[*]I = Incorrectly Set Machine = 1 - 0.7 = 0.3
[*]I|G = Incorrectly Set Machine And Good Part = 0.4
[*]B< = BAD PARTS = 0.60
[/LIST]
P[correctly set & part ok] = P(C) * P(C|G)
P[correctly set & part ok] = 70% * 90% = 63%
P[correctly set & part ok] = P(I) * P(I|G)
P[incorrectly set & part ok] = 30% *40% = 12%
P[correctly set | part ok] = P[correctly set & part ok]/(P[correctly set & part ok] + P[incorrectly set & part ok])
P[correctly set | part ok] = 63/(63+12) = [B]0.84 or 84%[/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]

Container Arrangements

Given a set of items inside a container, this calculates the probability that you draw certain items in the following fashion:

Draw__all__ the items

Draw__any of__ the items

How many ways can you choose m items of a, n items of b, o items of c, etc.

Draw

Draw

How many ways can you choose m items of a, n items of b, o items of c, etc.

Cost Recovery Method

Given a sales price, cost, and set of payments, this determines the gross profit per year based on the cost recovery method.

Country A produces about 7 times the amount of diamonds in carats produce in Country B. If the total

Country A produces about 7 times the amount of diamonds in carats produce in Country B. If the total produced in both countries is 40,000,000 carats, find the amount produced in each country.
Set up our two given equations:
[LIST=1]
[*]A = 7B
[*]A + B = 40,000,000
[/LIST]
Substitute (1) into (2)
(7B) + B = 40,000,000
Combine like terms
8B = 40,000,000
Divide each side by 8
[B]B = 5,000,000[/B]
Substitute this into (1)
A = 7(5,000,000)
[B]A = 35,000,000[/B]

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].

Cross Partitions

Given a set of partitions, this determines the cross partitions.

d is h decreased by 301

d is h decreased by 301
h decreased by 301 means we subtract 301 from h
h - 301
The phrase [I]is[/I] means equal to, so we set d equal to this expression:
[B]d = h - 301[/B]

D is the set of days in the week.

D is the set of days in the week.
[B]D = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}[/B]

d is the set of days of the week

d is the set of days of the week
[B]d = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}[/B]

d squared is greater than or equal to 17

d squared is greater than or equal to 17
d squared means we raise the variable d to the power of 2:
d^2
The phrase [I]greater than or equal to[/I] means an inequality. So we set this up using the >= in relation to 17:
[B]d^2 >= 17[/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]

Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of h

Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 26 cards left. How many cards did Dan start with?
Let the starting amount of cards be s. We're given:
[LIST]
[*]Dan bought 7 new cards: s + 7
[*]The dog ate half of his collection. This means he's left with half, or (s + 7)/2
[*]Now, he's got 26 cards left. So we set up the following equation:
[/LIST]
(s + 7)/2 = 26
Cross multiply:
s + 7 = 26 * 2
s + 7 = 52
To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B7%3D52&pl=Solve']we plug this equation into our search engine[/URL] and we get:
s = [B]45[/B]

Dan bought a computer in a state that has a sales tax rate of 7%. If he paid $67.20 sales tax, what

Dan bought a computer in a state that has a sales tax rate of 7%. If he paid $67.20 sales tax, what did the computer cost?
Set up the equation for price p:
p * 0.07 = 67.20
p = 67.20 / 0.07
p = [B]$960[/B]

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]

Daniel is 41 inches tall. He is 3/5 as tall as his brother. How tall is his brother?

Daniel is 41 inches tall. He is 3/5 as tall as his brother. How tall is his brother?
We set Daniel's brother's height at h. We have:
3h/5 = 41
To solve this equation for h, we [URL='https://www.mathcelebrity.com/prop.php?num1=3h&num2=41&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
[B]h = 68.3333 or 68 & 1/3[/B]

Daniel's gas tank holds n gallons of gas. How many pints does the tank hold?

Daniel's gas tank holds n gallons of gas. How many pints does the tank hold?
Setup conversion:
1 gallon = 8 pints
n gallons = [B]8n[/B] pints

Dave paints a fence in 4 hours while Sara paints the same fence in 2 hours. If they work together, h

Dave paints a fence in 4 hours while Sara paints the same fence in 2 hours. If they work together, how long will it take them to paint the fence?
Set up unit rates:
[LIST]
[*]Dave paints 1/4 of the fence in 1 hour
[*]Sara will paint 1/2 of the fence in 1 hour
[/LIST]
So together, they paint 1/2 + 1/4 = 2/4 + 14 = 3/4 of the fence in one hour.
1 hour = 60 minutes, so we set up a proportion of time to minutes where m is the time in minutes needed to complete 1 full fence:
3/4/60 = 1/m
3/240 = 1/m
[URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3&num2=1&den1=240&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion in our math engine[/URL], we get:
m = [B]80 minutes[/B]
[B]80 minutes is also 1 hour and 20 minutes.[/B]

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]

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]

Debra buys candy that costs 4 per pound. She will spend less than 20 on candy. What are the possible

Debra buys candy that costs 4 per pound. She will spend less than 20 on candy. What are the possible numbers of pounds she will buy?
Set up an inequality using less than < and p for pounds:
4p < 20
Divide each side by 4:
4p/4 < 20/4
[B]p < 5[/B]

Declining Balance Depreciation

Solves for Depreciation Charge, Asset Value, and Book Value using the Declining Balance Method

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]

Dennis was getting in shape for a marathon. The first day of the week he ran n miles. Dennis then ad

Dennis was getting in shape for a marathon. The first day of the week he ran n miles. Dennis then added a mile to his run each day. By the end of the week (7 days), he had run a total of 70 miles. How many miles did Dennis run the first day?
Setup distance ran for the 7 days:
[LIST=1]
[*]n
[*]n + 1
[*]n + 2
[*]n + 3
[*]n + 4
[*]n + 5
[*]n + 6
[/LIST]
Add them all up:
7n + 21 = 70
Solve for [I]n[/I] in the equation 7n + 21 = 70
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 21 and 70. To do that, we subtract 21 from both sides
7n + 21 - 21 = 70 - 21
[SIZE=5][B]Step 2: Cancel 21 on the left side:[/B][/SIZE]
7n = 49
[SIZE=5][B]Step 3: Divide each side of the equation by 7[/B][/SIZE]
7n/7 = 49/7
n =[B] 7
[URL='https://www.mathcelebrity.com/1unk.php?num=7n%2B21%3D70&pl=Solve']Source[/URL][/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]

Determine if the statement below is True or False

Determine if the statement below is True or False
If B ? A, then A ? B = B
Is this statement True or False?
[B]True:[/B] If B ? A, then B ? A
So A ? B is the similar elements of both. B contains itself as a subset.
So this is [U]true[/U]

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]

Diego is jogging at a rate of 5mi/h. A function relates how far Deigo jogs to his rate of speed.

Let d be distance and h be hours in time. Set up our function.
[LIST]
[*]f(h) = d
[*][B]f(h) = 5h[/B]
[/LIST]
Read this out, it says, for every hour Diego jogs, multiply that by 5 to get the distance he jogs.

Diegos savings increased by 9 is 68 . Use the variable to represent Diegos savings.

Diegos savings increased by 9 is 68 . Use the variable to represent Diegos savings.
Let Diego's savings be s.
The phrase [I]increased by[/I] means add, so we add 9 to s
s + 9
The phrase [I]is [/I]means equal to, so we set 2 + 9 = 68
[B]s + 9 = 68[/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

Difference between 23 and y is 12

Difference between 23 and y
23 - y
Is, means equal to, so we set 23 - y equal to 12
[B]23 - y = 12
[/B]
If you need to solve this algebraic expression, use our [URL='http://www.mathcelebrity.com/1unk.php?num=23-y%3D12&pl=Solve']equation calculator[/URL]:
[B]y = 11[/B]

Direct Current (Electrical Engineering) Ohms Law

Enter two of the following items from the DIRECT CURRENT(DC) electrical engineering set of variables, and this will solve for the remaining two:

* I = current(amps.)

* V = Electricity potential of voltage(volts)

* R = resistance(ohms)

* P = power(watts)

* I = current(amps.)

* V = Electricity potential of voltage(volts)

* R = resistance(ohms)

* P = power(watts)

Dollar Weighted Interest Method

Solves for Interest Rate, Starting Asset Value, Ending Asset Value, and Expenses using the Dollar Weighted Method.

Donna buys a bag of 11 oranges for 2.86. Find the unit price in dollars per orange.

Set up a proportion in dollars to oranges
2.86/11 oranges = x/1
[URL='http://www.mathcelebrity.com/unit-cost-calculator.php?num=11poundbagfor2.86&pl=Calculate+Unit+Cost']Using our unit cost calculator[/URL]
[B]0.26 per orange[/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]

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 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]

eana paid $5 for 20 lbs of bananas. how much were each pound?

$5 for 20 pounds equal = $x for 1 pound
Set up a proportion:
5/20 = x/1
[URL='http://www.mathcelebrity.com/prop.php?num1=5&num2=x&den1=20&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Use our proportion calculator[/URL]
x = 0.25

eight oranges are $1.00 how much would 5 dozen oranges cost?

eight oranges are $1.00 how much would 5 dozen oranges cost?
Set up a proportion of oranges to cost where c is the cost for 5 dozen = 60 oranges:
8/1 = 60/c
To solve this proportion, [URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=60&den1=1&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
c = [B]7.5[/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]

Erica is 5 feet tall and has a shadow of 2 feet. A nearby tree has a shadow of 18 feet. How tall is

Erica is 5 feet tall and has a shadow of 2 feet. A nearby tree has a shadow of 18 feet. How tall is the tree?
Set up a proportion of feet tall to shadow height where n is the height of the tree
5/2 = n/18
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5&num2=n&den1=2&den2=18&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
n =[B]45 feet[/B]

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.

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]

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]

Expand Master and Build Polynomial Equations

This calculator is the __ultimate__ expansion tool to multiply polynomials. It expands algebraic expressions listed below using all 26 variables (a-z) as well as negative powers to handle polynomial multiplication. Includes multiple variable expressions as well as outside multipliers.

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)^{x}

* Polynomial Expansions c(d + e + f)^{x}

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)

* Polynomial Expansions c(d + e + f)

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and

Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and sharing the same y-intercept
Get this in slope-intercept form by adding 5y to each side:
4x - 5y + 5y = 5y + 20
Cancel the 5y's on the left side and we get:
5y + 20 = 4x
Subtract 20 from each side
5y + 20 - 20 = 4x - 20
Cancel the 20's on the left side and we get:
5y = 4x - 20
Divide each side by 5:
5y/5 = 4x/5 - 4
y = 4x/5 - 4
So we have a slope of 4/5
to find our y-intercept, we set x = 0:
y = 4(0)/5 - 4
y = 0 - 4
y = -4
If we want a line perpendicular to the line above, our slope will be the negative reciprocal:
The reciprocal of 4/5 is found by flipping the fraction making the numerator the denominator and the denominator the numerator:
m = 5/4
Next, we multiply this by -1:
-5/4
So our slope-intercept of the perpendicular line with the same y-intercept is:
[B]y = -5x/4 - 4[/B]

Exponential Smoothing

Performs exponential smoothing on a set of data.

f(x)=a(b)^x and we know that f(3)=17 and f(7)=3156. what is the value of b

f(x)=a(b)^x and we know that f(3)=17 and f(7)=3156. what is the value of b
Set up both equations with values
When x = 3, f(3) = 17, so we have a(b)^3 = 17
When x = 7, f(7) = 3156, so we have a(b)^7 = 3156
Isolate a in each equation
a = 17/(b)^3
a = 3156/(b)^7
Now set them equal to each other
17/(b)^3 = 3156/(b)^7
Cross Multiply
17b^7 = 3156b^3
Divide each side by b^3
17b^4 = 3156
Divide each side by 17
b^4 = 185.6471
[B]b = 3.6912[/B]

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]

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 midpoint of the set of points (4,4) and (0,6)

Find the midpoint of the set of points (4,4) and (0,6)
We [URL='https://www.mathcelebrity.com/slope.php?xone=4&yone=4&slope=+2%2F5&xtwo=0&ytwo=6&pl=You+entered+2+points']type in (4,4) and (0,6) into our search engine [/URL]and we get:
Midpoint = [B](2, 5)[/B]

Find the subset of {a,b,c,d,e}

Find the subset of {a,b,c,d,e}
Using our power set calculator, we find [URL='https://www.mathcelebrity.com/powerset.php?num=a%2Cb%2Cc%2Cd%2Ce&pl=Show+Power+Set+and+Partitions']all the 32 subsets of {a,b,c,d,e}[/URL]

Find two consecutive positive integers such that the difference of their square is 25

Find two consecutive positive integers such that the difference of their square is 25.
Let the first integer be n. This means the next integer is (n + 1).
Square n: n^2
Square the next consecutive integer: (n + 1)^2 = n^2 + 2n + 1
Now, we take the difference of their squares and set it equal to 25:
(n^2 + 2n + 1) - n^2 = 25
Cancelling the n^2, we get:
2n + 1 = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B1%3D25&pl=Solve']Typing this equation into our search engine[/URL], we get:
n = [B]12[/B]

Find x

Find x
[IMG]https://mathcelebrity.com/community/data/attachments/0/cong-angles.jpg[/IMG]
Since both angles are congruent, we set them equal to each other:
6x - 20 = 4x
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x-20%3D4x&pl=Solve']type this equation into our math engine[/URL] and we get:
x = [B]10[/B]

Fishers Exact Test

Given a, b, c, and d, this calculates the probability of any such set of values using Fishers exact Test

Five sets of ear buds cost $53.15. How much will 9 sets of ear buds cost?

Five sets of ear buds cost $53.15. How much will 9 sets of ear buds cost?
Set up a proportion of earbuds to cost where c is the cost of 9 ear buds:
5/53.15 = 9/c
To solve this proportion for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=5&num2=9&den1=53.15&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
c = [B]95.67[/B]

Five times Kim's age plus 13 equals 58. How old is Kim?

Five times Kim's age plus 13 equals 58. How old is Kim?
Let Kim's age be a. We have:
Five times Kim's age:
5a
Plus 13 means we add 13
5a + 13
Equals 58 means we set the expression 5a + 13 equal to 58
5a + 13 = 58 <-- This is our algebraic expression
To solve this equation for a, [URL='https://www.mathcelebrity.com/1unk.php?num=5a%2B13%3D58&pl=Solve']we type it into our search engine[/URL] and get:
a = [B]9[/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.

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]

Frank averages 1 strike for every 4 frames that he bowls. If he bowled 48 strikes in 1 season, how m

Frank averages 1 strike for every 4 frames that he bowls. If he bowled 48 strikes in 1 season, how many frames did Frank bowl?
Set up a proportion of strikes to frames:
1/4 = 48/x
Run this through our [URL='http://www.mathcelebrity.com/prop.php?num1=1&num2=48&den1=4&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL]:
x = [B]192 frames[/B]

Function Test

Checks to see if a set of ordered pairs represents a function

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.

g equals 232 subtracted from the quantity 377 times g

g equals 232 subtracted from the quantity 377 times g
377 times g:
377g
232 subtracted from 377 times g:
377g - 232
We set the variable g equal to this expression:
[B]g = 377g - 232[/B]

g less than 143 is equal to 39 reduced by w

g less than 143 is equal to 39 reduced by w
g less than 143 means we subtract g from 143
143 - g
39 reduced by w means we subtract w from 39
39 - w
We set these 2 expressions equal to each other:
[B]143 - g = 39 - w[/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]

George and William both ran a one mile race. William won the race with a time of 4 minutes and 30 se

George and William both ran a one mile race. William won the race with a time of 4 minutes and 30 seconds. If George was 480 feet behind William when the race finished, how long did it take George to run the entire mile? (George continued to run at the same pace.)
When the race was done, George completed:
5280 feet in a mile - 480 feet = 4800 feet
set up a proportion of distance traveled to time where n is the time needed to run the mile
4800/4.5 = 5280/n
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=4800&num2=5280&den1=4.5&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
n = 4.95
5280/4800 = 1.1
Setup another proportion with the 1.1 factor of distance to time:
4800 * 1.1/4.5 * 1.1 = 5280/4.95
4.95 = 4 minutes and .95*60 seconds
4.95 = [B]4 minutes and 57 seconds[/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: 3(2x ? 5) = 15 Prove: x = 5

Given: 3(2x ? 5) = 15 Prove: x = 5
Set x = 5:
3(2(5) - 5)
3(10 - 5)
3(5)
15
So if x = 5, then:
3(2x ? 5) = 15

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 Factors of Monomials

This calculator will determine the Greatest Common Factors of a set of Monomials

Greg runs 120 m in 20 seconds. How far can he run in one minute?

Greg runs 120 m in 20 seconds. How far can he run in one minute?
We want to compare seconds to seconds.
[URL='https://www.mathcelebrity.com/timecon.php?quant=1&pl=Calculate&type=minute']1 minute[/URL] = 60 seconds
Set up a proportion of meters to seconds where m is the meters ran in 60 seconds:
120/20 = m/60
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=120&num2=m&den1=20&den2=60&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
m. = [B]360 meters[/B]

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 of g multiplied by t squared is equal to d.

Half of g multiplied by t squared is equal to d.
Half of g:
g/2
t squared:
t^2
Half of g multiplied by t squared:
gt^2/2
The phrase [I]is equal to[/I] mean we set gt^2/2 equal to d:
[B]gt^2/2 = d[/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]

Hans rented a truck for one day. There was a base fee of 16.95, and there was an additional charge o

Hans rented a truck for one day. There was a base fee of 16.95, and there was an additional charge of 76 cents for each mile driven. Hans had to pay 152.99 when he returned the truck. For how many miles did he drive the truck?
Set up the equation where x is the amount of miles he drove:
0.76x + 16.95 = 152.99
[URL='http://www.mathcelebrity.com/1unk.php?num=0.76x%2B16.95%3D152.99&pl=Solve']Plug this equation into our calculator[/URL]:
x = 179 miles

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.

Herfindahl Index

Given a market share of a set of companies, this determines the Herfindahl Index and Normalized Herfindahl Index.

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) 1800 is the cost to run the business for a day. To clarify, when you plug in x = 0 for 0 candy bars sold, you are left with -1,800, which is the cost of doing business for one day.
b) Maximum profit is found by taking the derivative of the profit equation and setting it equal to 0.
P'(x) = -0.002x + 3
With P'(x) = 0, we get:
-0.002x + 3 = 0
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=-0.002x%2B3%3D0&pl=Solve']equation solver[/URL], we get:
x = 1,500
To get maximum profit, we plug in x = 1,500 to our [I]original profit equation[/I]
P(1,500) = ? 0.001(1,500)^2 + 3(1,500) ? 1800
P(1,500) = -2,250 + 4,500 - 1,800
P(1,500) = $[B]450[/B]

Hose A can fill a pool in 4 hours. Hose B can fill the pool in 2 hours. If both hoses are turned on

Hose A can fill a pool in 4 hours. Hose B can fill the pool in 2 hours. If both hoses are turned on at the same time how long will it take to fill the pool?
[LIST]
[*]Hose A can fill the pool in 1/4 of the pool an hour
[*]Hose B can fill the pool in 1/2 of the pool an hour
[/LIST]
In one hour using combined effort, we have:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F2&frac2=1%2F4&pl=Add']1/2 + 1/4[/URL] = 3/4 of the pool will be filled.
3/4 of the pool gets filled in 60 minutes. We set up a proportion of proportion filled to time where t is the time to fill the full pool:
3/4/60 = 1/t
3/240 = 1/t
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3&num2=1&den1=240&den2=t&propsign=%3D&pl=Calculate+missing+proportion+value']proportion solver[/URL], we get:
t = [B]80 minutes or 1 hour and 20 minutes[/B]

How long will it take $3000 to earn $900 interest at 6% simple interest?

How long will it take $3000 to earn $900 interest at 6% simple interest?
Set up the simple interest equation for the interest piece:
3000 * 0.06t = 900
To solve for t in this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=3000%2A0.06t%3D900&pl=Solve']type it in our search engine [/URL]and we get:
t = [B]5[/B]

How many candles are in a box if 5 boxes have 100 candles?

How many candles are in a box if 5 boxes have 100 candles?
100 candles per 5 boxes. Set up a proportion:
100 candles/5 boxes = x candles / 1 box
Run this proportion [URL='https://www.mathcelebrity.com/prop.php?num1=100&num2=x&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']through our calculator[/URL]: 100/5 = x/1
x = [B]20[/B]

How many dimes must be added to a bag of 200 nickels so that the average value of the coins in the b

How many dimes must be added to a bag of 200 nickels so that the average value of the coins in the bag is 8 cents?
200 nickels has a value of 200 * 0.05 = $10.
Average value of coins is $10/200 = 0.05
Set up our average equation, where we have total value divided by total coins:
(200 * 0.05 + 0.1d)/(200 + d) = 0.08
Cross multiply:
16 + 0.08d = 10 + 0.1d
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=16%2B0.08d%3D10%2B0.1d&pl=Solve']equation solver[/URL], we get:
[B]d = 300[/B]

How many factors does 36 have

How many factors does 36 have
We can type in [URL='https://www.mathcelebrity.com/factoriz.php?num=36&pl=Show+Factorization']factor 36[/URL] into our math engine and we get:
{1, 2, 3, 4, 6, 9, 12, 18, 36}
1 * 36
2 * 18
3 * 12
4 * 9
6 * 6
This set contains [B]9 factors[/B].

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 do 10 pieces of candy cost if 1000 pieces cost 100.00?

How much do 10 pieces of candy cost if 1000 pieces cost 100.00?
Set up a proportion of pieces to cost
10/x = 1000/100
Divide the right side by 100 on top and bottom
10/x = 10/1
[B]x = 1[/B]

How old am I if 400 reduced by 3 times my age is 124?

How old am I if 400 reduced by 3 times my age is 124?
Let my age be a. We're given an algebraic expression:
[LIST]
[*]3 times my age means we multiply a by 3: 3a
[*]400 reduced by 3 times my age means we subtract 3a from 400:
[*]400 - 3a
[*]The word [I]is[/I] mean an equation, so we set 400 - 3a equal to 124
[/LIST]
400 - 3a = 124
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D124&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]92[/B]

How old am I if: 210 reduced by 3 times my current age is 4 times my current age?

How old am I if: 210 reduced by 3 times my current age is 4 times my current age?
Let your current age be a. We're given:
[LIST]
[*]210 reduced by 3 times current age = 210 - 3a
[*]4 times current age = 4a
[*]The word [I]is[/I] means equal to. So we set 210 - 3a equal to 4a
[/LIST]
210 - 3a = 4a
To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=210-3a%3D4a&pl=Solve']type this equation into our search engine [/URL]and we get:
a = [B]30[/B]

How old am I of 400 reduced by 2 times my age is 224

How old am I of 400 reduced by 2 times my age is 224
[LIST=1]
[*]Let my age be a.
[*]2 times my age: 2a
[*]400 reduced by 2 times my age: 400 - 2a
[*]The phrase [I]is [/I]means an equation. So we set 400 - 2a equal to 224 for our algebraic expression
[/LIST]
[B]400 - 2a = 224
[/B]
If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D224&pl=Solve']type this equation into our search engine[/URL] and we get:
a = [B]88[/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 $11.60, all dimes and quarters, in my pocket. I have 32 more dimes than quarters. how many di

I HAVE $11.60, all dimes and quarters, in my pocket. I have 32 more dimes than quarters. how many dimes, and how many quarters do i have?
Let d = dimes and q = quarters.
We have two equations:
[LIST=1]
[*]0.10d + 0.25q = 11.60
[*]d - q = 32
[/LIST]
Set up a [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=0.10d+%2B+0.25q+%3D+11.60&term2=d+-+q+%3D+32&pl=Cramers+Method']system of equations[/URL] to solve for d and q.
[B]dimes (d) = 56 and quarters (q) = 24[/B]
Check our work:
56 - 24 = 32
0.10(56) + 0.25(24) = $5.60 + $6.00 = $11.60

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 100 runners went with 4 bicyclists and 5 walkers, how many bicyclists would go with 20 runners an

If 100 runners went with 4 bicyclists and 5 walkers, how many bicyclists would go with 20 runners and 2 walkers?
[U]Set up a joint variation equation, for the 100 runners, 4 bicyclists, and 5 walkers:[/U]
100 = 4 * 5 * k
100 = 20k
[U]Divide each side by 20[/U]
k = 5 <-- Coefficient of Variation
[U]Now, take scenario 2 to determine the bicyclists with 20 runners and 2 walkers[/U]
20 = 2 * 5 * b
20 = 10b
[U]Divide each side by 10[/U]
[B]b = 2[/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 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 3 pounds of apples cost 0.90, how much will 10 pounds cost?

Set up a proportion of apples to cost, where a is the unknown cost amount of apples for 10 pounds
3/0.90 = 10/c
Use our [URL='http://www.mathcelebrity.com/prop.php?num1=3&num2=10&den1=0.90&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL]:
[B]c = 3[/B]

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 3/15 is equivalent to 45/a, find a

if 3/15 is equivalent to 45/a, find a.
Set up the proportion:
3/15 = 45/a
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=45&den1=15&den2=a&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
a = [B]225[/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 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 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integ

If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integer.
[LIST]
[*]Let the integer be "x".
[*]Square the integer: x^2
[*]7 times the square: 7x^2
[*]5 times the integer: 5x
[*]Add them together: 7x^2 + 5x
[*][I]The result is[/I] means an equation, so we set 7x^2 + 5x equal to 2
[/LIST]
7x^2 + 5x = 2
[U]This is a quadratic equation. To get it into standard form, we subtract 2 from each side:[/U]
7x^2 + 5x - 2 = 2 - 2
7x^2 + 5x - 2 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=7x%5E2%2B5x-2%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get two solutions:
[LIST=1]
[*]x = 2/7
[*]x= -1
[/LIST]
The problem asks for an integer, so our answer is x[B] = -1[/B].
[U]Let's check our work by plugging x = -1 into the quadratic:[/U]
7x^2 + 5x - 2 = 0
7(-1)^2 + 5(-1) - 2 ? 0
7(1) - 5 - 2 ? 0
0 = 0
So we verified our answer, [B]x = -1[/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 800 feet of fencing is available, find the maximum area that can be enclosed.

If 800 feet of fencing is available, find the maximum area that can be enclosed.
Perimeter of a rectangle is:
2l + 2w = P
However, we're given one side (length) is bordered by the river and the fence length is 800, so we have:
So we have l + 2w = 800
Rearranging in terms of l, we have:
l = 800 - 2w
The Area of a rectangle is:
A = lw
Plug in the value for l in the perimeter into this:
A = (800 - 2w)w
A = 800w - 2w^2
Take the [URL='https://www.mathcelebrity.com/dfii.php?term1=800w+-+2w%5E2&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']first derivative[/URL]:
A' = 800 - 4w
Now set this equal to 0 for maximum points:
4w = 800
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%3D800&pl=Solve']Typing this equation into the search engine[/URL], we get:
w = 200
Now plug this into our perimeter equation:
l = 800 - 2(200)
l = 800 - 400
l = 400
The maximum area to be enclosed is;
A = lw
A = 400(200)
A = [B]80,000 square feet[/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 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 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 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 rock rolled n meters, how many decimeters did it roll?

If a rock rolled n meters, how many decimeters did it roll?
Setup conversion
1 meter = 10 decimeters
Therefore, n meters is [B]10n[/B] decimeters

If a speedometer indicates that a car is traveling at 65 kilometers per hour, how fast is the car tr

If a speedometer indicates that a car is traveling at 65 kilometers per hour, how fast is the car traveling in miles per hour? (Round to the nearest tenth.)
Set up a proportion of miles per kilometers:
0.621/1 = n/65
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=0.621&num2=n&den1=1&den2=65&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
n = [B]40.365[/B]

If a universal set contains 250 elements, n(A) = 90, n(B) = 125, and n(A ? B) = 35, find n(A ? B)'.

If a universal set contains 250 elements, n(A) = 90, n(B) = 125, and n(A ? B) = 35, find n(A ? B)'.
We know from set theory that:
n(A U B) = n(A) + n(B) - n(A ? B)
Plugging in our given values, we get:
n(A U B) = 90 + 125 - 35
n(A U B) = 180
The problem asks for n(A U B)'. This formula is found with:
n(A U B)' = n(U) - n(A U B)
n(U) is the universal set which is 250, so we have:
n(A U B)' = 250 - 180
n(A U B)' = [B]70[/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 ballons are on sale at 15 for$3, whats the cost for a ballon? a)50cents b)25cost c)20cents d)20 d

if ballons are on sale at 15 for$3, whats the cost for a ballon? a)50cents b)25cost c)20cents d)20 dollars
Let c be the cost of 1 balloon. We set up a proportion of balloons to cost:
15/3 = 1/c
To solve this proportion for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=1&den1=3&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
c = [B]0.2 or 20 cents[/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 f(x) = 3 - 2x and g(x) = 1/x + 5 what is the value of (f/g)(8)?

If f(x) = 3 - 2x and g(x) = 1/x + 5 what is the value of (f/g)(8)?
Set up (f/g)(x)
(3 - 2x)/(1/x + 5)
Now find (f/g)(8)
(3 - 2(8))/(1/8+ 5)
(3 - 16)/(5.125)
-13/5.125
[B]2.5366[/B]

If f={(4,2),(5,1),(6,2),(7,3),(8,6)} then the range of f is what

If f={(4,2),(5,1),(6,2),(7,3),(8,6)} then the range of f is what
The range is the full set of all possible y-values:
{1, 2, 2, 3, 6}
Remove duplicates, we get:
[B]{1, 2, 3, 6}[/B]

if g(x) =5x + 3 and g(a) = 14, then what is the value of a?

if g(x) =5x + 3 and g(a) = 14, then what is the value of a?
We set g(a) = 5a + 3 = 14
5a + 3 = 14
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=5a%2B3%3D14&pl=Solve']equation solver[/URL], we get:
a = [B]2.2[/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 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 it takes 3/4 cup of flour to make 10 pancakes, how much flour will it take to make 40 pancakes

If it takes 3/4 cup of flour to make 10 pancakes, how much flour will it take to make 40 pancakes?
Set up a proportion of flour to pancakes:
3/4/10 = x/40
3/4 is 0.75, so use our [URL='http://www.mathcelebrity.com/prop.php?num1=0.75&num2=x&den1=10&den2=40&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL]:
[B]x = 3[/B]

If it takes 6.6 pounds of seed to plant one acre of grass, how many acres can be planted with 9.24 p

If it takes 6.6 pounds of seed to plant one acre of grass, how many acres can be planted with 9.24 pounds of seed.
Set up a proportion, seed to acre:
6.6/1 = 9.24/x
Using our proportion calculator, we get [B]x = 1.4[/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 p is inversely proportional to the square of q, and p is 2 when q is 4, determine p when q is equ

If p is inversely proportional to the square of q, and p is 2 when q is 4, determine p when q is equal to 2.
We set up the variation equation with a constant k such that:
p = k/q^2 [I](inversely proportional means we divide)
[/I]
When q is 4 and p is 2, we have:
2 = k/4^2
2 = k/16
Cross multiply:
k = 2 * 16
k = 32
Now, the problem asks for p when q = 2:
p = 32/2^2
p = 32/4
p = [B]8[/B]

If power is big, you can assume:

If power is big, you can assume:
a. The difference between the means is more likely to be detected
b. The significance level set by the researcher must be high
c. We increase the probability of type I error
d. Your study result will be more likely to be inconclusive
[B]b. The significance level set by the researcher must be high[/B]

If set A ={1,2,3,4} and B={2,4,6,8}, what is A intersect B

If set A ={1,2,3,4} and B={2,4,6,8}, what is A intersect B
Using our [URL='https://www.mathcelebrity.com/setnotation.php?num1=1%2C2%2C3%2C4&num2=2%2C4%2C6%2C8&pl=Set+Notation+Items']set notation calculator[/URL], we get:
A intersect B = [B]{2, 4}[/B]

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 ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?

if the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?
Set up our given ratio:
2x/5y = 3/4
Cross multiply:
2x * 4 = 5y * 3
8x = 15y
Divide each side by 8:
8x/8 = 15y/8
x = 15y/8
Now divide each side by y to find x/y:
x/y = 15y/8y
x/y =[B] 15/8[/B]

If the temperature during the day is 6° and the temperature drops 15° after sunset, what is the temp

If the temperature during the day is 6° and the temperature drops 15° after sunset, what is the temperature at night?
A drop in temperature means we subtract, so we have:
6 - 15 = [B]-9 or 9 below zero[/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 angles are supplementary and congruent then they are right angles

if two angles are supplementary and congruent then they are right angles
Let the first angle be x. Let the second angle be y.
Supplementary angles means their sum is 180:
x + y = 180
We're given both angles are congruent, meaning equal. So we set x = y:
y + y = 180
To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=y%2By%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
y = [B]90. <-- 90 degrees is a right angle, so this is TRUE[/B]

If x is 18 when y is 6, find y when x is 21

If x is 18 when y is 6, find y when x is 21
Set up a proportion of x to y:
18/6 = 21/y
To solve this proportion for y, we[URL='https://www.mathcelebrity.com/prop.php?num1=18&num2=21&den1=6&den2=y&propsign=%3D&pl=Calculate+missing+proportion+value'] type it in our search engine[/URL] and we get:
y = [B]7[/B]

If y=2x and y=18, what is the value of x

If y=2x and y=18, what is the value of x
Since y = 2x [B]and[/B] y = 18, we set 2x equals to 18 since they both equal y
2x = 18
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D18&pl=Solve']Type this equation into our search engine[/URL] and we get:
x = [B]9[/B]

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 add 7 to 2x, the result is 17

if you add 7 to 2x, the result is 17
Add 7 to 2x:
2x + 7
The phrase [I]the result is[/I] means an equation, so we set 2x + 7 = 17
[B]2x + 7 = 17 [/B] <-- This is our algebraic expression
Now, if you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B7%3D17&pl=Solve']type in 2x + 7 = 17 into the search engine[/URL], and we get [B]x = 5[/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 can buy one of pineapple chunks for $2 then how many can you buy with $10

Set up a proportion of pineapple chunks to dollars:
1/2 = x/10
Use our [URL='http://www.mathcelebrity.com/prop.php?num1=1&num2=x&den1=2&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL]:
[B]x = 5[/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 have 65$, how many pots can you buy, the pots are 3x + 10

If you have 65$, how many pots can you buy, the pots are 3x + 10
Set 3x + 10 = 65 and solve for x:
3x + 10 = 65
Plugging this into our equation calculator, we get:
x = [B]18.33[/B]

If you multiply me by 33 and subtract 20, the result is 46. Who am I?

If you multiply me by 33 and subtract 20, the result is 46. Who am I?
[LIST]
[*]Start with the variable x
[*]Multiply me by 33 = 33x
[*]Subtract 20: 33x - 20
[*]The result is 46, means we set this expression equal to 46: 33x - 20 = 46
[/LIST]
Run this through our [URL='http://www.mathcelebrity.com/1unk.php?num=33x-20%3D46&pl=Solve']equation calculator[/URL], and we get:
[B]x = 2[/B]

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 1996 Ato Boldon of UCLA ran the 100-meter dash in 9.92 seconds. In 1969 John Carlos of San Jose S

In 1996 Ato Boldon of UCLA ran the 100-meter dash in 9.92 seconds. In 1969 John Carlos of San Jose State ran the 100-yard dash in 9.1 seconds. Which runner had the faster average speed?
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=100&type=yard&pl=Calculate']convert yards to meters using our conversion calculator[/URL] and we get:
100 yards = 91.44 meters
Now we set up a proportion of time per meter:
[LIST]
[*]Ato Boldon: 9.92/100 = 0.992 per meter
[*]John Carlos: 9.1/91.44 = 0.995 per meter
[/LIST]
[B]Since Ato Boldon's time was [I]less per meter[/I], he had the faster average speed[/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 8 years kelly's age will be twice what it is now. How old is kelly?

In 8 years kelly's age will be twice what it is now. How old is kelly?
Let Kelly's age be a.
In 8 years means we add 8 to a:
a + 8
Twice means we multiply a by 2:
2a
The phrase [I]will be[/I] means equal to, so we set a + 8 equal to 2a
a + 8 = 2a
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B8%3D2a&pl=Solve']type it in our math engine[/URL] and we get:
a = [B]8
[/B]
[U]Evaluate a = 8 and check our work[/U]
8 + 8 ? 2(8)
16 = 16
[MEDIA=youtube]y4jaQpkaJEw[/MEDIA]

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 certain lot, there are 16 white, 7 red, 8 blue, and 9 black cars. You randomly pick a set of ke

In a certain lot, there are 16 white, 7 red, 8 blue, and 9 black cars. You randomly pick a set of keys to one of the cars. What is the probability of choosing a set of keys to a blue car?
[U]Our total cars are:[/U]
Total Cars = White Cars + Red Cars + Blue Cars = Black Cars
Total Cars = 16 + 7 + 8 + 9
Total Cars = 40
P(Blue) = Blue Cars / Total Cars
P(Blue) = 8/40
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F40&frac2=3%2F8&pl=Simplify']fraction simplify calculator[/URL], we get:
P(Blue) = [B]1/5[/B]

In the year 1999, Hicham El Guerrouj of Morocco set a new world record when he ran a mile in 3 minut

In the year 1999, Hicham El Guerrouj of Morocco set a new world record when he ran a mile in 3 minutes 43.13 seconds. What was his speed in miles per hour? (Round your answer to the nearest hundredth.)
3 minutes = 60 seconds per minute = 180 seconds
180 seconds + 43.13 seconds = 223.13 seconds
223.13 seconds/3600 seconds per hour = 1 mile/n miles
Cross multiply:
223.13n = 3600
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=223.13n%3D3600&pl=Solve']equation solver[/URL], we get:
n = [B]16.13 miles per hour[/B]

Interpolation

Given a set of data, this interpolates using the following methods:

* Linear Interpolation

* Nearest Neighbor (Piecewise Constant)

* Polynomial Interpolation

* Linear Interpolation

* Nearest Neighbor (Piecewise Constant)

* Polynomial Interpolation

Interval Counting

Evaluates a set of interval counting statements in the form a(b)c.

Interval Notation and Set Builder Notation

This calculator translates the following inequality statements to interval notation and set builder notation:

* x < 5

* y <= 5

* z > 5

* a >= 5

* b < 5 or b > 20

* Compound Inequality such as 0 <= c < 4

* |x|<3

* Reverse Interval Notation to Inequality Statement such as (-7,5]

* {x|x<1}

* Word representations of interval notations such as 2 is less than or equal to x is less than or equal to 8

* x < 5

* y <= 5

* z > 5

* a >= 5

* b < 5 or b > 20

* Compound Inequality such as 0 <= c < 4

* |x|<3

* Reverse Interval Notation to Inequality Statement such as (-7,5]

* {x|x<1}

* Word representations of interval notations such as 2 is less than or equal to x is less than or equal to 8

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]

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 recommended that a ladder be placed 2 feet away from the Wall for every 5 feet of height. How

It is recommended that a ladder be placed 2 feet away from the Wall for every 5 feet of height. How far from the Wall should a 20 foot ladder be placed?
Set up a proportion:
2ft away from the wall / 5ft = (x)ft away from the wall / 20ft
[URL='http://www.mathcelebrity.com/prop.php?num1=2&num2=x&den1=5&den2=20&propsign=%3D&pl=Calculate+missing+proportion+value']Run this proportion through our calculator by typing[/URL]: 2/5=x/20
x = [B]8 ft[/B]

It takes 3 city snowplows 14 hours to clear 500 miles of road. If the city wants the 500 miles of ro

It takes 3 city snowplows 14 hours to clear 500 miles of road. If the city wants the 500 miles of road to be cleared in 6 hours, how many additional snowplows must they buy?
Set up unit rate per plow:
14 hours * 3 plows = 42 hours for one plow to clear 500 miles of road
Calculate the amount of plows we need:
42 hours / 6 hours = 7 plows
Additional plows = New plows - original plows:
Additional plows = 7 - 3
Additional plows = [B]4[/B]

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]

jake did 92 sit-ups each day that he exercised. if he exercised every day for 4 weeks approximately

jake did 92 sit-ups each day that he exercised. if he exercised every day for 4 weeks approximately how many setups did he do?
7 days per week * 4 weeks = 28 days
92 sit-ups per day * 28 days = 2,576 sit-ups

Jake used 5 boxes to pack 43.5 kg of books. If the boxes each weighed the same and held 8 books, wh

Jake used 5 boxes to pack 43.5 kg of books. If the boxes each weighed the same and held 8 books, what did each book weigh?
[U]Set up equations were w is the weight of each book:[/U]
[LIST=1]
[*]5 boxes * 8 books * w = 43.5
[*]40w = 43.5
[/LIST]
[U]Divide each side by 40[/U]
[B]w = 1.0875 kg[/B]

jamie needs 3 cups of flour and 4 cups of sugar how many cups of sugar will she need if she uses 9 c

jamie needs 3 cups of flour and 4 cups of sugar how many cups of sugar will she need if she uses 9 cups of flour?
Set up a proportion of flour/sugar:
3/4 = 9/x
[URL='http://www.mathcelebrity.com/prop.php?num1=3&num2=9&den1=4&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']Cross multiply or enter that into the search engine[/URL]
3x = 36
[B]x = 12[/B]

Jason wrote a total of 8 pages over 2 hours. How many hours will Jason have to spend writing this we

Jason wrote a total of 8 pages over 2 hours. How many hours will Jason have to spend writing this week in order to have written a total of 12 pages? Assume the relationship is directly proportional.
Set up a proportion of pages to hours
8 pages/2 hours = 12 pages/x hours
enter 8/2 = 12/x into the [URL='http://www.mathcelebrity.com/prop.php?num1=8&num2=12&den1=2&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']search engine[/URL]:
[B]x = 3[/B]

Jenny added $150 to her savings account in July. At the end if the month she had $500. How much did

Jenny added $150 to her savings account in July. At the end if the month she had $500. How much did she start with?
Let the starting balance be s. A deposit means we added 150 to s to get 500. We set up this equation below:
s + 150 = 500
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B150%3D500&pl=Solve']type this equation into our search engine[/URL] and we get:
s = 3[B]50[/B]

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 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.

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]

Jessica tutors chemistry. For each hour that she tutors, she earns 30 dollars. Let E be her earnings

Jessica tutors chemistry. For each hour that she tutors, she earns 30 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H . Then use this equation to find Jessicas earnings after tutoring for 19 hours.
Set up a function of h hours for tutoring:
[B]E(h) = 30h[/B]
We need to find E(19)
E(19) = 30(19)
E(19) = [B]570[/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]

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 buys 9 cds for the same price, he also buys a dvd for 20. His total bill is 119. Find the cost o

Joe buys 9 cds for the same price, he also buys a dvd for 20. His total bill is 119. Find the cost of one cd.
[U]Let c be the cost of one CD. Set up the equation:[/U]
9c + 20 = 119
[U]Use the [URL='http://www.mathcelebrity.com/1unk.php?num=9c%2B20%3D119&pl=Solve']equation solver[/URL]:[/U]
[B]c = 11[/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]

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 mows 3 lawns in 4 hours, Paul mows 5 lawns in 6 hours. Who mows faster?

John mows 3 lawns in 4 hours, Paul mows 5 lawns in 6 hours. Who mows faster?
To see who mows faster, we set up fractions with a common denominator.
You can see this by running this statement in the calculator:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3/4&frac2=5/6&pl=Compare']3/4 or 5/6[/URL]
You'll see that 5/6 is larger, so Paul mores more lawns per hour.

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]

Johnny Rocket can run 300 meters in 90 seconds. If his speed remains constant, how far could he ru

Johnny Rocket can run 300 meters in 90 seconds. If his speed remains constant, how far could he run in 500 seconds? Round to one decimal place.
Set up the distance equation:
Distance = Rate * Time
300 = 90r
Solving this equation for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=300%3D90r&pl=Solve']type it in our search engine[/URL] and we get:
r = 3.333
For 500 seconds, we set up our distance equation again:
Distance = 500 * 3.333333
Distance = [B]1666.7 meters[/B]

Joint Variation Equations

Given a joint variation (jointly proportional) of a variable between two other variables with a predefined set of conditions, this will create the joint variation equation and solve based on conditions.
Also called combined variation.

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15%

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month?
[U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
10% written as a decimal is 0.1. We want decimals to solve equations easier.
S(m) = 0.1m + 1500
[U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
15% written as a decimal is 0.15. We want decimals to solve equations easier.
S(m) = 0.15m + 1200
[U]The question asks what is m when both S(m)'s equal each other[/U]:
The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other
0.1m + 1500 = 0.15m + 1200
We want to isolate m terms on one side of the equation.
Subtract 1200 from each side:
0.1m + 1500 - 1200 = 0.15m + 1200 - 1200
Cancel the 1200's on the right side and we get:
0.1m - 300 = 0.15m
Next, we subtract 0.1m from each side of the equation to isolate m
0.1m - 0.1m + 300 = 0.15m - 0.1m
Cancel the 0.1m terms on the left side and we get:
300 = 0.05m
Flip the statement since it's an equal sign to get the variable on the left side:
0.05m = 300
To solve for m, we divide each side of the equation by 0.05:
0.05m/0.05 = 300/0.05
Cancelling the 0.05 on the left side, we get:
m = [B]6000[/B]

Jow buys 9 CD’s for the same price, and also a cassette tape for $9.45. His total bill was 118.89. W

Jow buys 9 CD’s for the same price, and also a cassette tape for $9.45. His total bill was 118.89. What was the cost of one CD?
Let the price of each cd be c. We're given the equation:
9c + 9.45 = 118.89
[URL='https://www.mathcelebrity.com/1unk.php?num=9c%2B9.45%3D118.89&pl=Solve']We type this equation into our search engine[/URL] and we get:
c = [B]12.16[/B]

Julia has a bucket of water that weighs 10lbs. The total weight is 99% water. She leaves the bucke

Julia has a bucket of water that weighs 10lbs. The total weight is 99% water. She leaves the bucket outside overnight and some of the water evaporates, in the morning the water is only 98% of the total weight. What is the new weight?
Setup the proportion:
0.99/10 = 0.98/w
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=0.99&num2=0.98&den1=10&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]w = 9.899 lbs[/B].

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]

k equals the sum of h and 23

The sum of h and 23 means we add:
h + 23
k equals means we set our expression above equal to k
h + 23 = k

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]

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.

Kartek bought 86 pizzas for a school party. If there are 516 people at his school, how much pizza sh

Kartek bought 86 pizzas for a school party. If there are 516 people at his school, how much pizza should each person get?
Setup unit slices:
[URL='https://www.mathcelebrity.com/search.php?q=86%2F516']86 pizzas / 516 people[/URL] = [B]1/6 pizza per person[/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].

Kendrick set his watch 9 seconds behind, and it falls behind another 1 second everyday.How far behin

Kendrick set his watch 9 seconds behind, and it falls behind another 1 second everyday.How far behind is Kendrick's watch if he last set it 23 days ago?
Seconds Behind = 9 seconds behind + 1 second everyday * 23 days
Seconds Behind = 9 + 23
Seconds Behind = 32

Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The tot

Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The total value of the jar is $7.85. How many of each type?
Let d be dimes and q be quarters. Set up two equations from our givens:
[LIST=1]
[*]d + q = 41
[*]0.1d + 0.25q = 7.85
[/LIST]
[U]Rearrange (1) by subtracting q from each side:[/U]
(3) d = 41 - q
[U]Now, substitute (3) into (2)[/U]
0.1(41 - q) + 0.25q = 7.85
4.1 - 0.1q + 0.25q = 7.85
[U]Combine q terms[/U]
0.15q + 4.1 = 7.85
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.15q%2B4.1%3D7.85&pl=Solve']equation calculator[/URL], we get:[/U]
[B]q = 25[/B]
[U]Substitute q = 25 into (3)[/U]
d = 41 - 25
[B]d = 16[/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]

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]

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].

kyle baked 29 muffins. He placed p muffins each in 4 boxes and had 5 muffins left over. How many muf

kyle baked 29 muffins. He placed p muffins each in 4 boxes and had 5 muffins left over. How many muffins were in each box
We set up the following equation:
4p + 5 = 29
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=4p%2B5%3D29&pl=Solve']type it in our math engine[/URL] and we get:
p = [B]6[/B]

L is the set of letters in the word Mississippi

L is the set of letters in the word Mississippi
We want only unique letters, so we have:
[B]L = {I, M, P, S}[/B]

Lauren wrote a total of 6 pages over 2 hours. How many hours will Lauren have to spend writing this

Lauren wrote a total of 6 pages over 2 hours. How many hours will Lauren have to spend writing this week in order to have written a total of 9 pages? Solve using unit rates.
6 pages per 2 hours equals 6/2 = 3 pages per hour as a unit rate
Set up equation using h hours:
3h = 9
Divide each side by 3
[B]h = 3[/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

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 U be the set of all integers between ?3 and 3 (including ?3 and 3). Let A={?2,0,1,3}. Find Ac. G

Let U be the set of all integers between ?3 and 3 (including ?3 and 3). Let A={?2,0,1,3}. Find Ac. Give your answer in standard set notation
Ac is anything not in A, but in U. So we have:
Ac = [B]{-3, -1, 2}[/B]

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]

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]

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.

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]

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 the set of integers that are greater than or equal to -1 and less than or equal to 2

M is the set of integers that are greater than or equal to -1 and less than or equal to 2
We include -1 on the left, and include 2 on the right
[B]M = {-1, 0, 1, 1, 2)[/B]

M is the sum of a and its reciprocal

M is the sum of a and its reciprocal
The reciprocal of a variable is 1 divided by the variable
1/a
The sum of a and its reciprocal means we add:
a + 1/a
The phrase [I]is[/I] means an equation, so we set M equal to the sum of a + 1/a:
[B]M = 1 + 1/a[/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]

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. How many did she start with?
Take this in parts
[LIST=1]
[*]Maria starts with b boxes.
[*]She buys seven more. So she has b + 7 boxes
[*]A week later, half of all her boxes are destroyed in a fire. Which means she's left with 1/2. (b + 7)/2
[*]Now she has 22 boxes. So we set (b + 7)/2 = 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']Typing this equation into our search engine and solving for b[/URL], we get:
[B]b = 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]

Marion Middle School has 600 students. Mike surveys a random sample of 30 students and finds that 7

Marion Middle School has 600 students. Mike surveys a random sample of 30 students and finds that 7 of them play a musical instrument. How many students at the school are likely to play a musical instrument?
Set up a proportion of those that play musical instruments to total students where m is the amount of students in the 600 who play a musical instrument:
7/30 = m/600
[URL='https://www.mathcelebrity.com/prop.php?num1=7&num2=m&den1=30&den2=600&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
m = [B]140[/B]

Marita's nose is 2 inches long and her head is 9 inches tall. Assume Mount Rushmore was carved using

Marita's nose is 2 inches long and her head is 9 inches tall. Assume Mount Rushmore was carved using the same ratio. If Teddy Roosevelt's head is 60 feet tall, how long should his nose be? Round to the nearest foot, if necessary.
Set up a proportion/ratio of head height to nose height where n is the nose height for 60 feet head height:
9/2 = 60/n
[U]Using our [URL='https://www.mathcelebrity.com/prop.php?num1=9&num2=60&den1=2&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we see that:[/U]
n = [B]13.33 rounded to the nearest foot is 13 feet[/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 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 Written Assignment

Im sorta confused about this question?
He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this.
Here is (most of) the information you asked for:
[LIST]
[*]Is he redoing the whole yard or just the front?
He's redoing the whole yard
[*]How much topsoil does he need?
I'm not sure, you'll have to figure that out. Remember he's putting a new 4 inch layer down over all the area currently covered by grass in the overhead picture above.
[*]How big is the yard?
I'm not sure, but you can probably estimate it using the overhead picture.
[*]What kind of pickup truck does he drive?
A 2003 Ford F-150 XL.
[*]How much can the pickup carry?
The truck bed is 80 inches long, 69 inches wide, and 20 inches tall.
[*]How much is the delivery charge?
$30 per truckload on top of the soil cost. Each truckload can deliver up to 18 cubic yards.
[*]How much does the topsoil cost?
$18 per cubic yard (sold in 1/4 yard increments).
[*]How far is the soil store?
It is 9 miles away. It takes about 20 minutes to drive there.
[*]What gas mileage does the pickup truck get?
It averages 17 miles to the gallon.
[*]What is the current gas cost?
Assume it's $3.79/gallon.
[/LIST]
Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery?
Detail all your assumptions and calculations, and clearly write out your final conclusions.

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 cat weighs 10 pounds more than his pet hamster. His dog weighs the same as his cat. If the

Matthew's cat weighs 10 pounds more than his pet hamster. His dog weighs the same as his cat. If the weight of all three pets is 35 pounds, ow much does his hamster weigh?
Setup weights and relations:
[LIST]
[*]Hamster weight: w
[*]Cat weight: w + 10
[*]Dog weight:w + 10
[/LIST]
Add all the weights up:
w + w + 10 + w + 10 = 35
Solve for [I]w[/I] in the equation w + w + 10 + w + 10 = 35
[SIZE=5][B]Step 1: Group the w terms on the left hand side:[/B][/SIZE]
(1 + 1 + 1)w = 3w
[SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE]
10 + 10 = 20
[SIZE=5][B]Step 3: Form modified equation[/B][/SIZE]
3w + 20 = + 35
[SIZE=5][B]Step 4: Group constants:[/B][/SIZE]
We need to group our constants 20 and 35. To do that, we subtract 20 from both sides
3w + 20 - 20 = 35 - 20
[SIZE=5][B]Step 5: Cancel 20 on the left side:[/B][/SIZE]
3w = 15
[SIZE=5][B]Step 6: Divide each side of the equation by 3[/B][/SIZE]
3w/3 = 15/3
w =[B] 5[/B]
[B]
[URL='https://www.mathcelebrity.com/1unk.php?num=w%2Bw%2B10%2Bw%2B10%3D35&pl=Solve']Source[/URL][/B]

Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00 bob bought 3 burgers and

Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00. Bob bought 3 burgers and 1 drink for $5.50. How much is each burger and drink?
[U]Set up the givens where b is the cost of a burger and d is the cost of a drink:[/U]
Max: 2b + 2d = 5
Bob: 3b + d = 5.50
[U]Rearrange Bob's equation by subtracting 3b from each side[/U]
(3) d = 5.50 - 3b
[U]Now substitute that d equation back into Max's Equation[/U]
2b + 2(5.50 - 3b) = 5
2b + 11 - 6b = 5
[U]Combine b terms:[/U]
-4b + 11 = 5
[U]Subtract 11 from each side[/U]
-4b = -6
[U]Divide each side by -4[/U]
b = 3/2
[B]b = $1.50[/B]
[U]Now plug that back into equation (3):[/U]
d = 5.50 - 3(1.50)
d = 5.50 - 4.50
[B]d = $1.00[/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]

Method of Equated Time-Exact Method-Macaulay Duration-Volatility

Given a set of cash flows at certain times, and a discount rate, this will calculate t using the equated time method and the exact method, as well as the macaulay duration and volatility

Michelle can paint one car in 2 hours. It takes Tyler 3 hours to paint the same car while Colton tak

Michelle can paint one car in 2 hours. It takes Tyler 3 hours to paint the same car while Colton takes 6 hours to paint the car. If they all work together, how long will it take them to paint the car?
Setup unit rates:
[LIST]
[*]Michelle can paint 1/2 of the car in one hour
[*]Tyler can paint 1/3 of the car in one hour
[*]Colton can paint 1/6 of the car in one hour
[/LIST]
In one hour using a combined effort, they can paint:
1/2 + 1/3 + 1/6 = 6/6 = 1 car in [B]one hour[/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]

Missing Average

Given a set of scores and an average, this calculates the next score necessary to attain that average

Modified Internal Rate of Return (MIRR)

Given a set of positive/negative cash flows, a finance rate, and a reinvestment rate, this calculates the modified internal rate of return

Modified Payback Period

Given a set of cash inflows, outflows, and a discount rate, this calculates the modified payback period.

Months with 31 days as set M

Months with 31 days as set M
Our cardinality of this set is 7, as show below:
{[B]January, March, May, July, August, October, December[/B]}

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. 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. 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. 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

Ms. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngest

Ms. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngest and the middle son gets $35 more than the youngest, how much does each boy get?
Let 0 be the oldest son, m be the middle sun, and y be the youngest son. Set up our given equations
[LIST]
[*]o = 2y
[*]m = y + 35
[*]o + m + y = 975
[/LIST]
[U]Substitute the first and second equations into Equation 3[/U]
2y + y + 35 + y = 975
[U]Combine the y terms[/U]
4y + 35 = 975
Subtract 35 using our [URL='http://www.mathcelebrity.com/1unk.php?num=4y%2B35%3D975&pl=Solve']equation calculator[/URL] to solve and get [B]y = 235[/B]
[U]Plug y = 235 into equation 2[/U]
m = 235 + 35
[B]m = 270[/B]
[U]Plug y = 235 into equation 2[/U]
o = 2(235)
[B]o = 470[/B]

Multinomial Distribution

Given a set of x_{i} counts and a respective set of probabilities θ_{i}, this calculates the probability of those events occurring.

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.

n is a factor of 16

n is a factor of 16
List out factor of 16:
1 * 16
2 * 8
4 * 4
From the list above, we take the 5 [U]unique[/U] factors and build a set for n:
n = [B]{1, 2, 4, 8, 16}[/B]

n is equal to 135 less than the quantity 61 times n

n is equal to 135 less than the quantity 61 times n
61 times n:
61n
135 less than the quantity 61 times n
61n - 135
We set n equal to this expression:
[B]n = 61n - 135[/B]

n is equal to the product of 7 and the sum of m and 6

n is equal to the product of 7 and the sum of m and 6
The sum of m and 6:
m + 6
The product of 7 and this sum:
7(m + 6)
We set this expression equal to n:
[B]7(m + 6) = n[/B]

n is the sum of twenty-five and fifteen

n is the sum of twenty-five and fifteen
The sum of twenty-five and fifteen:
25 + 15
The word [I]is[/I] means an equal to, so we set 25 + 15 equal to n:
[B]n = 25 + 15
n = 40[/B]

N reduced by 2 is the same as Z increased by 7

N reduced by 2 is the same as Z increased by 7
[LIST]
[*]N reduced by 2 means subtract --> n - 2
[*]z increased by 7 means add --> z + 7
[*][I]Is the same as[/I] means equal to, so we set these expressions equal to each other
[*][B]n - 2 = z + 7[/B]
[/LIST]

Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daug

Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daughter?
Declare variables for each age:
[LIST]
[*]Let Nancy's age be n
[*]Let her daughter's age be d
[/LIST]
We're given two equations:
[LIST=1]
[*]n = 3d - 10
[*]n = 41
[/LIST]
We set 3d - 10 = 41 and solve for d:
Solve for [I]d[/I] in the equation 3d - 10 = 41
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants -10 and 41. To do that, we add 10 to both sides
3d - 10 + 10 = 41 + 10
[SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE]
3d = 51
[SIZE=5][B]Step 3: Divide each side of the equation by 3[/B][/SIZE]
3d/3 = 51/3
d = [B]17[/B]

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]

Nate jars 2 liters of jam everyday. How many days did Nate spend making jam if he jarred 8 liters of

Nate jars 2 liters of jam everyday. How many days did Nate spend making jam if he jarred 8 liters of jam?
2 liters per 1 day and 8 liters per x days.
Set up a proportion:
2/1 = 8/x
Cross multiply:
2x = 8
Divide each side by 2
x = [B]4 days[/B].

Natural Numbers

Shows a set amount of natural numbers and cumulative sum

Need Help on this problem

What do you want to do with this number set? Express it as representation of integers?

Nick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that show

Nick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that shows how much money Nick has after x amount of days.
Set up the function M(x) where M(x) is the amount of money after x days. Since spending means a decrease, we subtract to get:
[B]M(x) = 50 - 5x[/B]

nine times x is twice the sum of x and five

nine times x is twice the sum of x and five
Take this algebraic expression in 4 pieces:
[U]Step 1: nine time x:[/U]
9x
[U]Step 2: The sum of x and five means we add 5 to x:[/U]
x + 5
[U]Step 3: The word [I]twice[/I] means we multiply the sum x + 5 by 2:[/U]
2(x + 5)
[U]Step 4: The word [I]is[/I] means equal to, so we set 9x equal to 2(x + 5) to get our final algebraic expression of:[/U]
[B]9x = 2(x + 5)[/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].

Normal body temperature is 98.6 ? F. Write an inequality that describes the temperature

Normal body temperature is 98.6 ? F. Write an inequality that describes the temperature, T, of people with above normal temperatures.
Above means greater than, so we set up the inequality:
[B]T > 98.6 ?[/B]

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 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].

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]

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]

Omar's classroom has 2 closets. Each closet has 3 shelves. There are 5 backpacks on each shelf.

Omar's classroom has 2 closets. Each closet has 3 shelves. There are 5 backpacks on each shelf.
2 closets * 3 shelves per closet * 5 backpacks per shelf = [B]30 backpacks[/B]

On a map, every 5 cm represents 250 kilometres. What distance would be represented by a 3 cm line?

On a map, every 5 cm represents 250 kilometres. What distance would be represented by a 3 cm line?
We set up a proportion of map cm distance to kilometers where k is the kilometers represented by a 3cm line
5/250 = 3/k
To solve this proportion for k, we [URL='https://www.mathcelebrity.com/prop.php?num1=5&num2=3&den1=250&den2=k&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
k = [B]150[/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 an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two

On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two grades was 138. Find the lowest grade.
[U]Let h be the highest grade and l be the lowest grade. Set up the given equations:[/U]
(1) h = l + 42
(2) h + l = 138
[U]Substitute (1) into (2)[/U]
l + 42 + l = 138
[U]Combine l terms[/U]
2l + 42 = 138
[U]Enter that equation into our [URL='http://www.mathcelebrity.com/1unk.php?num=2l%2B42%3D138&pl=Solve']equation calculator[/URL] to get[/U]
[B]l = 48
[/B]
[U]Substitute l = 48 into (1)[/U]
h = 48 + 42
[B]h = 90[/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]

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]

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].

p decreased by 65 is the same as the total of f and 194

p decreased by 65 is the same as the total of f and 194
p decreased by 65
p - 65
The total of f and 194
f + 194
The phrase [I]is the same as[/I] means equal to, so we set the expressions above equal to each other
[B]p - 65 = f + 194[/B]

p is equal to r plus 2 times q

p is equal to r plus 2 times q
2 times q:
2q
r plus 2 times q:
r + 2q
is equal to means we set p equal to r + 2q
[B]p = r + 2q[/B]

Parallel Resistors

Given a set of parallel resistors, this calculates the total resistance in ohms, denoted R_{t}

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]

Payback Period

Given a set of cash inflows and cash outflows at certain times, this determines the net cash flow, cumulative cash flow, and payback period

Penelope and Owen work at a furniture store. Penelope is paid $215 per week plus 3.5% of her total s

Penelope and Owen work at a furniture store. Penelope is paid $215 per week plus 3.5% of her total sales in dollars, xx, which can be represented by g(x)=215+0.035x. Owen is paid $242 per week plus 2.5% of his total sales in dollars, xx, which can be represented by f(x)=242+0.025x. Determine the value of xx, in dollars, that will make their weekly pay the same.
Set the pay functions of Owen and Penelope equal to each other:
215+0.035x = 242+0.025x
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=215%2B0.035x%3D242%2B0.025x&pl=Solve']equation calculator[/URL], we get:
[B]x = 2700[/B]

People with a drivers license are at least 16 years old and no older than 85 years old

People with a drivers license are at least 16 years old and no older than 85 years old.
Set up the inequality, where p represents the people:
[LIST=1]
[*]The phrase [I]at least[/I] means greater than or equal to. So we use the >= sign. 16 <= p
[*]The phrase [I]no older than[/I] means less than or equal to. So we use the <= sign. p <= 85
[/LIST]
Combine these inequalities, and we get:
[B]16 <= p <= 85[/B]
To see the interval notation for this inequality and all possible values, visit the [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=16%3C%3Dp%3C%3D85&pl=Show+Interval+Notation']interval notation calculator[/URL].

Percentiles

Given a set of scores and a target score, this will determine the percentile of the target score using two different formulas.

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

Permutations with Replacement

Calculates the following:

How many permutations can we have from a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed?

How many permutations can we have from a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed?

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

Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Sup

Pleasantburg has a population growth model of P(t)=at^2+bt+P0 where P0 is the initial population. Suppose that the future population of Pleasantburg t years after January 1, 2012, is described by the quadratic model P(t)=0.7t^2+6t+15,000. In what month and year will the population reach 19,200?
Set P(t) = 19,200
0.7t^2+6t+15,000 = 19,200
Subtract 19,200 from each side:
0.7t^2+6t+4200 = 0
The Quadratic has irrational roots. So I set up a table below to run through the values. At t = 74, we pass 19,200. Which means we add 74 years to 2012: 2012 + 74 = [B]2086[/B]
t 0.7t^2 6t Add 15000 Total
1 0.7 6 15000 15006.7
2 2.8 12 15000 15014.8
3 6.3 18 15000 15024.3
4 11.2 24 15000 15035.2
5 17.5 30 15000 15047.5
6 25.2 36 15000 15061.2
7 34.3 42 15000 15076.3
8 44.8 48 15000 15092.8
9 56.7 54 15000 15110.7
10 70 60 15000 15130
11 84.7 66 15000 15150.7
12 100.8 72 15000 15172.8
13 118.3 78 15000 15196.3
14 137.2 84 15000 15221.2
15 157.5 90 15000 15247.5
16 179.2 96 15000 15275.2
17 202.3 102 15000 15304.3
18 226.8 108 15000 15334.8
19 252.7 114 15000 15366.7
20 280 120 15000 15400
21 308.7 126 15000 15434.7
22 338.8 132 15000 15470.8
23 370.3 138 15000 15508.3
24 403.2 144 15000 15547.2
25 437.5 150 15000 15587.5
26 473.2 156 15000 15629.2
27 510.3 162 15000 15672.3
28 548.8 168 15000 15716.8
29 588.7 174 15000 15762.7
30 630 180 15000 15810
31 672.7 186 15000 15858.7
32 716.8 192 15000 15908.8
33 762.3 198 15000 15960.3
34 809.2 204 15000 16013.2
35 857.5 210 15000 16067.5
36 907.2 216 15000 16123.2
37 958.3 222 15000 16180.3
38 1010.8 228 15000 16238.8
39 1064.7 234 15000 16298.7
40 1120 240 15000 16360
41 1176.7 246 15000 16422.7
42 1234.8 252 15000 16486.8
43 1294.3 258 15000 16552.3
44 1355.2 264 15000 16619.2
45 1417.5 270 15000 16687.5
46 1481.2 276 15000 16757.2
47 1546.3 282 15000 16828.3
48 1612.8 288 15000 16900.8
49 1680.7 294 15000 16974.7
50 1750 300 15000 17050
51 1820.7 306 15000 17126.7
52 1892.8 312 15000 17204.8
53 1966.3 318 15000 17284.3
54 2041.2 324 15000 17365.2
55 2117.5 330 15000 17447.5
56 2195.2 336 15000 17531.2
57 2274.3 342 15000 17616.3
58 2354.8 348 15000 17702.8
59 2436.7 354 15000 17790.7
60 2520 360 15000 17880
61 2604.7 366 15000 17970.7
62 2690.8 372 15000 18062.8
63 2778.3 378 15000 18156.3
64 2867.2 384 15000 18251.2
65 2957.5 390 15000 18347.5
66 3049.2 396 15000 18445.2
67 3142.3 402 15000 18544.3
68 3236.8 408 15000 18644.8
69 3332.7 414 15000 18746.7
70 3430 420 15000 18850
71 3528.7 426 15000 18954.7
72 3628.8 432 15000 19060.8
73 3730.3 438 15000 19168.3
74 3833.2 444 15000 19277.2

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 help!!

It is a set theory question

Please help!!

(1) |P(A)| = 4 <-- Cardinality of the power set is 4, which means we have 2^n = 4.[B] |A| = 2
[/B]
(2) |B| = |A|+ 1 and |A×B| = 30
|B| = 6 if [B]|A| = 5[/B] and |A x B| = 30
(3) |B| = |A|+ 2 and |P(B)|?|P(A)| = 24
Since |B| = |A|+ 2, we have: 2^(a + 2) - 2^a = 24
2^a(2^2 - 1) = 24
2^a(3) = 24
2^a = 8
[B]|A |= 3[/B]
To check, we have |B| = |A| + 2 --> 3 + 2 = 5
So |P(B)| = 2^5 = 32
|P(A)| = 2^3 = 8
And 32 - 8 = 24

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]

Portfolio Rate of Return

Given a portfolio of individual assets with returns and weights, this calculates the total portfolio rate of return.

power set for S= {b,c,f}

power set for S= {b,c,f}
The [I]power set[/I] P is the set of all subsets of S including S and the empty set ?.
Since S contains 3 terms, our Power Set should contain 2^3 = 8 items
[URL='https://www.mathcelebrity.com/powerset.php?num=b%2Cc%2Cf&pl=Show+Power+Set+and+Partitions']Link to power set for this problem[/URL]
P = [B]{{}, {b}, {c}, {f}, {b,c}, {b,f}, {c,f}, {b,c,f}}[/B]

Power Sets and Set Partitions

Given a set S, this calculator will determine the power set for S and all the partitions of a set.

PRIVATE SAT TUTORING - LIVE FACE-TO-FACE SKYPE TUTORING

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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]

q is equal to 207 subtracted from the quantity 4 times q

q is equal to 207 subtracted from the quantity 4 times q
4 time q
4q
207 subtracted from 4 times q:
4q - 207
Set this equal to q:
[B]4q - 207 = q [/B]<-- This is our algebraic expression
To solve for q, [URL='https://www.mathcelebrity.com/1unk.php?num=4q-207%3Dq&pl=Solve']type this equation into the search engine[/URL]. We get:
[B]q = 69[/B]

r less than 164 is 248 more than the product of 216 and r

r less than 164 is 248 more than the product of 216 and r
[U]r less than 164:[/U]
164 - r
[U]The product of 216 and r:[/U]
216r
[U]248 more than the product of 216 and r[/U]
216r + 248
[I]The word is means an equation, so we set 164 - r equal to 216r + 248[/I]
[B]164 - r = 216r + 248[/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]

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.

Random Test

Given a set of data and an α value, this determines the test statistic and accept/reject hypothesis based on randomness of a dataset.

Rates of Return

Given a set of stock prices and dividends if applicable, this calculates the periodic rate of return and the logarithmic rate of return

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]

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]

Rita has spent $16 so far on gifts. The additional amount she will spend will be less than $14. What

Rita has spent $16 so far on gifts. The additional amount she will spend will be less than $14. What are the possible total amounts she will spend?
Rita will spend at least another cent on other gifts above the $16 she spent so far, but no more than $14. Also, the problem says less than 14. 16 + 14 is 30, so that is the top end of her spending.
Let's say her remaining spending is s. Set up the inequality for possible spending values.
[B]16 < s < 30[/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]

Roster Notation

Given a set of numbers, this displays the roster notation

sales 45,000 commission rate is 3.6% and salary is $275

sales 45,000 commission rate is 3.6% and salary is $275
Set up the commission function C(s) where s is the salary:
C(s) = Commission * s + salary
We're given: C(s) = 45,000, commission = 3.6%, which is 0.036 and salary = 275, so we have:
0.036s + 275 = 45000
To solve for s, we type this equation into our search engine and we get:
s = [B]1,242,361.11[/B]

Sales tax is directly proportional to cost. If the sales tax on a 46000 automobile is $240, what is

Sales tax is directly proportional to cost. If the sales tax on a 46000 automobile is $240, what is the sales tax on a $9000 automobile?
Set up a proportion of sales tax to purchase price where s is the sales tax on a 9000 automobile:
240/46000 = s/9000
[URL='https://www.mathcelebrity.com/prop.php?num1=240&num2=s&den1=46000&den2=9000&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL] and we get:
s = [B]46.96[/B]

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]

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'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]

Sample Space Probability

Given a sample space S and an Event Set E, this calculates the probability of the event set occuring.

Sara opened an account with $800 and withdrew $20 per week. Jordan opened an account with $500 and d

Sara opened an account with $800 and withdrew $20 per week. Jordan opened an account with $500 and deposited $30 per week. In how many weeks will their account be equal?
Each week, Sara's account value is:
800 - 20w <-- Subtract because Sara withdraws money each week
Each week, Jordan's account value is:
500 + 30w <-- Add because Jordan deposits money each week
Set them equal to each other:
800 - 20w = 500 + 30w
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=800-20w%3D500%2B30w&pl=Solve']equation solver[/URL], we get w = 6.
Check our work:
800 - 20(6)
800 - 120
680
500 + 30(6)
500 + 180
680

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]

Set B is the set of distinct letters in the word GIFT

Set B is the set of distinct letters in the word GIFT
Set B has 4 elements below:
B = [B]{G, I, F, T}[/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]

Set of all consonants in the word,'SECONDARY'

Set of all consonants in the word,'SECONDARY'
Our set has 6 elements below:
[B]{C, D, N, R, S, Y}[/B]

set of all continents

set of all continents
Our set of 7 elements is below:
{[B]Africa, Antarctica, Asia, Australia/Oceania, Europe, North America, and South America[/B].}

set of all letters in Australia

set of all letters in Australia
We remove duplicate "a's" and treat A and a as the same letters. Our set S is:
S = [B]{a, i, l, r, s, t, u}[/B]
If we want to find the properties of this set, we visit our [URL='https://www.mathcelebrity.com/powerset.php?num=%7Ba%2Ci%2Cl%2Cr%2Cs%2Ct%2Cu%7D&pl=Show+Power+Set']set notation calculator[/URL].

Set of consonants in the word EDUCATION

Set of consonants in the word EDUCATION
Consonants are all letters not vowels, so anything that is not {A, E, I, O, U}
Our set of consonants in the word EDUCATION is:
[B]{C, D, N, T}[/B]

set of days with the letter n

set of days with the letter n
We have the set below:
{Mo[B]n[/B]day, Wed[B]n[/B]esday, Su[B]n[/B]day}

set of vowels in the word ALGEBRA

set of vowels in the word ALGEBRA
Vowels are A, E, I, O, U.
For ALGEBRA, we have A, E, A
We group the 2 A's together, so our answer is:
[B]{A, E}[/B]

Set Theory Notation

Evaluates and describes various set theory notation

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

Sets

This lesson walks you through what a set is, how to write a set, elements of a set, types of sets, cardinality of a set, complement of a set.

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]

Sharpe Ratio

Calculates the Sharpe ratio given return on assets, risk free rate, and standard deviation

She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.9

She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.94, what was the price for a large pizza?
[U]Determine additional amount the pizzas would have cost without the coupon[/U]
6 pizzas * 3 per pizza = 18
[U]Add 18 to our discount price of 38.94[/U]
Full price for 6 large pizzas = 38.94 + 18
Full price for 6 large pizzas = 56.94
Let x = full price per pizza before the discount. Set up our equation:
6x = 56.94
Divide each side by 6
[B]x = $9.49[/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]

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.

Sinking Fund Depreciation Method

Using the Sinking Fund method of Depreciation, this calculator determines the following:

* Depreciation at time t (D_{t})

* Asset Value (A)

* Salvage Value (S)

* Book Value at time t (B_{t})

* Depreciation at time t (D

* Asset Value (A)

* Salvage Value (S)

* Book Value at time t (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

Six ounces of canned fish in oil has 396 calories. How many calories does 1 ounce have?

Set up a proportion of ounces to calories:
6/396 = 1/x <-- x is the amount of calories in one ounce
Run this through the [URL='http://www.mathcelebrity.com/prop.php?num1=6&num2=1&den1=396&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL]:
[B]x = 66[/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]

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is runn

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is running at 5 feet per second and Claire is running at 3 feet per second.
i. After how many seconds will Sophie catch Claire?
ii. If the race is 500 feet, who wins?
i.
Sophie's distance formula is given as D = 5s
Claire's distance formula is given as D = 3s + 100
Set them equal to each other
5s = 3s + 100
Subtract 3s from both sides:
2s = 100
Divide each side by 2
[B]s = 50[/B]
ii. [B]Sophie since after 50 seconds, she takes the lead and never gives it back.[/B]

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]

Stacy sells art prints for $12 each. Her expenses are $2.50 per print, plus $38 for equipment. How m

Stacy sells art prints for $12 each. Her expenses are $2.50 per print, plus $38 for equipment. How many prints must she sell for her revenue to equal her expenses?
Let the art prints be p
Cost function is 38 + 2p
Revenue function is 12p
Set cost equal to revenue
12p = 38 + 2p
Subtract 2p from each side
10p = 38
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=10p%3D38&pl=Solve']equation calculator[/URL] gives us [B]p = 3.8[/B]

States that begin with the letter C

States that begin with the letter C
Our set has 3 elements:
[B]{California, Colorado, Connecticut}[/B]

Straight Line Depreciation

Solves for Depreciation Charge, Asset Value, Salvage Value, Time, N, and Book Value using the Straight Line Method.

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]

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 5 times h and twice g is equal to 23

sum of 5 times h and twice g is equal to 23
Take this [U]algebraic expressions[/U] problem in pieces.
Step 1: 5 times h:
5h
Step 2: Twice g means we multiply g by 2:
2g
Step 3: sum of 5 times h and twice g means we add 2g to 5h
5h + 2g
Step 4: The phrase [I]is equal to[/I] means an equation, so we set 5h + 2g equal to 23:
[B]5h + 2g = 23[/B]

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 the Years Digits (SOYD) Depreciation

Solves for Depreciation Charge, Asset Value, and Book Value using the Sum of the Years Digits Method

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 17 inches of wire costs 51 cents at the same rate, how many inches of wire can be bough

Suppose that 17 inches of wire costs 51 cents at the same rate, how many inches of wire can be bought for 42 cents?
Set up a proportion of inches of wire to cost, were w equals the inches of wire at 42 cents. We have:
17/51 = w/42
[URL='https://www.mathcelebrity.com/prop.php?num1=17&num2=w&den1=51&den2=42&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], we get:
[B]w = 14[/B]

Suppose that h(x) varies directly with x and h(x)=44 when x = 2. What is h(x) when x = 1.5?

Suppose that h(x) varies directly with x and h(x)=44 when x = 2. What is h(x) when x = 1.5?
Direct variation means we set up an equation:
h(x) = kx where k is the constant of variation.
For h(x) = 44 when x = 2, we have:
2k = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=2k%3D44&pl=Solve']Type this equation into our search engine[/URL], we get:
k = 22
The question asks for h(x) when x = 1.5. So we set up our variation equation, knowing that k = 22.
kx = h(x)
With k = 22 and x = 1.5, we get:
22(1.5) = h(x)
h(x) = [B]33[/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].

Survival Rates

Given a set of times and survival population counts, the calculator will determine the following:

Survival Population l_{x}

Mortality Population d_{x}

Survival Probability p_{x}

Mortality Probability q_{x}

In addition, the calculator will determine the probability of survival from t_{x} to t_{x + n}

Survival Population l

Mortality Population d

Survival Probability p

Mortality Probability q

In addition, the calculator will determine the probability of survival from t

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]

Tabular Display

Enter a set of x and p(x) in a tabular probability distribution format and this will evaluate if it is valid or not.

Tamara can proofread 16 pages in 8 minutes. How many minutes will it take her to proofread 108 pages

Tamara can proofread 16 pages in 8 minutes. How many minutes will it take her to proofread 108 pages
Set up a proportion of pages to minutes:
16 pages/8 minutes = 108 pages / p minutes
We want to solve for p.
Type [I][URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=108&den1=8&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']16/8 = 108/p[/URL][/I] into the search engine.
We get p = [B]54 minutes[/B]

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 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 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 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 precipitation for the first 7 months of the year is 19.32 inches with a standard deviati

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed.
a. What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months?
b. What is the average precipitation of 5 randomly selected years for the first 7 months?
c. What is the probability of 5 randomly selected years will have an average precipitation greater than 18 inches for the first 7 months?
[URL='https://www.mathcelebrity.com/probnormdist.php?xone=18&mean=19.32&stdev=2.4&n=1&pl=P%28X+%3E+Z%29']For a. we set up our z-score for[/URL]:
P(X>18) = 0.7088
b. We assume the average precipitation of 5 [I]randomly[/I] selected years for the first 7 months is the population mean ? = 19.32
c. [URL='https://www.mathcelebrity.com/probnormdist.php?xone=18&mean=19.32&stdev=2.4&n=5&pl=P%28X+%3E+Z%29']P(X > 18 with n = 5)[/URL] = 0.8907

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 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 buffet at a restaurant is different for adults and kids. the bill for 2 adults and 3 k

the cost of a buffet at a restaurant is different for adults and kids. the bill for 2 adults and 3 kids is $51. the bill for 3 adults and 1 kid is $45. what is the cost per adult and per kid?
Let the cost for each adult be a
Let the cost for each kid be k
We're given two equations:
[LIST=1]
[*]2a + 3k = 51
[*]3a + k = 45
[/LIST]
To solve this simultaneous set of equations, we can use three methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*]a = [B]12[/B]
[*]k = [B]9[/B]
[/LIST]

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 gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a ga

The cost of a gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a gallon of milk cost 3.75, what is the cost of a gallon of water?
We're given:
m = 5w + 0.50
m = $3.75
Set them equal to each other:
5w + 0.50 = 3.75
[URL='https://www.mathcelebrity.com/1unk.php?num=5w%2B0.50%3D3.75&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 0.65[/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 renting a rototiller is $19.50 for the first hour and $7.95 for each additional hour. Ho

The cost of renting a rototiller is $19.50 for the first hour and $7.95 for each additional hour. How long can a person have the rototiller if the cost must be less than $95?
Setup the inequality:
$19.50 + $7.95x < $95
Subtract 19.50 from both sides:
7.95x < 75.50
Divide each side of the inequality by 7.95 to isolate x
x < 9.5
The next lowest integer is 9. So we take 9 + the first hour of renting to get [B]10 total hours[/B].
Check our work:
$7.95 * 9.5 + $19.50
$71.55 + $19.50 = $91.05

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 pounds of pork at $4.10 a pound

the cost of x pounds of pork at $4.10 a pound
Set up the cost function for pounds of pork:
[B]C(x) = 4.10x[/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 cube of x is less than 15

The cube of x is less than 15
The cube of x means we raise x to the 3rd power:
x^3
Less than 15 means we setup the following inequality
[B]x^3 < 15[/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 a and b is 10

The difference between a and b is 10.
The problem asks for an algebraic expression. Let's take each piece one by one:
[I]Difference between[/I] means we subtract:
a - b
The phrase [I]is [/I]means an equation, so we set a - b equal to 10
[B]a - b = 10[/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 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 in Julies height and 9 is 48 letting j be Julie's height

The difference in Julies height and 9 is 48 letting j be Julie's height
Step 1: If Julie's height is represented with the variable j, then we subtract 9 from j since the phrase [I]difference[/I] means we subtract:
j - 9
Step 2: The word [I]is[/I] means an equation, so we set j - 9 equal to 48 for our final algebraic expression:
[B]j - 9 = 48[/B]

The difference of 100 and x is 57

The difference of 100 and x means we subtract x from 100:
100 - x
Is means equal to, so we set our expression above equal to 57
[B]100 - x = 57
[/B]
If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=100-x%3D57&pl=Solve']equation calculator[/URL]

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 x and 5 is 2 times of x

the difference of x and 5 is 2 times of x
The difference of x and 5 means we subtract 5 from x
x - 5
The word [I]is[/I] means an equation, so we set x - 5 equal to 2 times x
[B]x - 5 = 2x[/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 first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The seco

The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The second plan had a $21 monthly fee and charges an additional $.10 for each minute of calls. For how many minutes of calls will the cost of the two plans be equal?
Set up the cost equation C(m) for the first plan, where m is the amount of minutes you use
C(m) = 0.14m + 14
Set up the cost equation C(m) for the second plan, where m is the amount of minutes you use
C(m) = 0.10m + 21
Set them equal to each other:
0.14m + 14 = 0.10m + 21
[URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B14%3D0.10m%2B21&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = [B]175[/B]

The function f(x) = x^3 - 48x has a local minimum at x = and a local maximum at x = ?

The function f(x) = x^3 - 48x has a local minimum at x = and a local maximum at x = ?
f'(x) = 3x^2 - 48
Set this equal to 0:
3x^2 - 48 = 0
Add 48 to each side:
3x^2 = 48
Divide each side by 3:
x^2 = 16
Therefore, x = -4, 4
Test f(4)
f(4) = 4^3 - 48(4)
f(4) = 64 - 192
f(4) = [B]-128 <-- Local minimum[/B]
Test f(-4)
f(-4) = -4^3 - 48(-4)
f(-4) = -64 + 192
f(-4) = [B]128 <-- Local maximum[/B]

The function P(x) = -30x^2 + 360x + 785 models the profit, P(x), earned by a theatre owner on the ba

The function P(x) = -30x^2 + 360x + 785 models the profit, P(x), earned by a theatre owner on the basis of a ticket price, x. Both the profit and the ticket price are in dollars. What is the maximum profit, and how much should the tickets cost?
Take the [URL='http://www.mathcelebrity.com/dfii.php?term1=-30x%5E2+%2B+360x+%2B+785&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']derivative of the profit function[/URL]:
P'(x) = -60x + 360
We find the maximum when we set the profit derivative equal to 0
-60x + 360 = 0
Subtract 360 from both sides:
-60x = -360
Divide each side by -60
[B]x = 6 <-- This is the ticket price to maximize profit[/B]
Substitute x = 6 into the profit equation:
P(6) = -30(6)^2 + 360(6) + 785
P(6) = -1080 + 2160 + 785
[B]P(6) = 1865[/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 height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +3

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +300. Find the average velocity of the object during the first 3 seconds? (b) Use the Mean value Theorem to verify that at some time during the first 3 seconds of the fall the instantaneous velocity equals the average velocity. Find that time.
Average Velocity:
[ f(3) - f(0) ] / ( 3 - 0 )
Calculate f(3):
f(3) = -4.9(3^2) + 300
f(3) = -4.9(9) + 300
f(3) = -44.1 + 300
f(3) = 255.9
Calculate f(0):
f(0) = -4.9(0^2) + 300
f(0) = 0 + 300
f(0) = 300
So we have average velocity:
Average velocity = (255.9 - 300)/(3 - 0)
Average velocity = -44.1/3
Average velocity = -[B]14.7
[/B]
Velocity is the first derivative of position
s(t)=-4.9t^2 +300
s'(t) = -9.8t
So we set velocity equal to average velocity:
-9.8t = -14.7
Divide each side by -9.8 to solve for t, we get [B]t = 1.5[/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 lowest temperature on may 15 is 2/3 as warm as the warmest temperature on may 15. the lowest tem

the lowest temperature on may 15 is 2/3 as warm as the warmest temperature on may 15. the lowest temperature on may 15 is 60F what is the warmest temperature on may 15?
Set up an equation where w is the warmest temperature on May 15:
60 = 2/3w
[URL='https://www.mathcelebrity.com/1unk.php?num=60%3D2%2F3w&pl=Solve']Type this equation into our search engine[/URL], and we get:
w = [B]90[/B]

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. Wh

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. What is the age of the person who entered the room?
The mean formulas is denoted as:
Mean = Sum of Ages / Total People
We're given Mean = 38 and Total People = 5, so we plug in our numbers:
28 = Sum of Ages / 5
Cross multiply, and we get:
Sum of Ages = 28 * 5
Sum of Ages = 140
One more person enters the room. The mean age is now 39. Set up our Mean formula:
Mean = Sum of Ages / Total People
With a new Mean of 39 and (5 + 1) = 6 people, we have:
39 = Sum of Ages / 6
But the new sum of Ages is the old sum of ages for 5 people plus the new age (a):
Sum of Ages = 140 + a
So we have:
29 = (140 + a)/6
Cross multiply:
140 + a = 29 * 6
140 + a = 174
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D174&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]34[/B]

The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?

The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?
Set up the perimeter equation:
2l + 2w = P
Given P = 204 and l = 66, we have:
2(66) + 2w = 204
2w + 132 = 204
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B132%3D204&pl=Solve']equation solver,[/URL] we get w = [B]36[/B].

The perimeter of a rectangular field is 250 yards. If the length of the field is 69 yards, what is

The perimeter of a rectangular field is 250 yards. If the length of the field is 69 yards, what is its width?
Set up the rectangle perimeter equation:
P = 2l + 2w
For l = 69 and P = 250, we have:
250= 2(69) + 2w
250 = 138 + 2w
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B138%3D250&pl=Solve']equation solver[/URL], we get:
[B]w = 56 [/B]

The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s length

The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s length?
Set up the perimeter (P) of a rectangle equation given length (l) and width (w):
2l + 2w = P
We're given P = 300 and w = 59. Plug these into the perimeter equation:
2l + 2(59) = 300
2l + 118 = 300
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B118%3D300&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]l = 91[/B]

The phone company charges Rachel 12 cents per minute for her long distance calls. A discount company

The phone company charges Rachel 12 cents per minute for her long distance calls. A discount company called Rachel and offered her long distance service for 1/2 cent per minute, but will charge a $46 monthly fee. How many minutes per month must Rachel talk on the phone to make the discount a better deal?
Minutes Rachel talks = m
Current plan cost = 0.12m
New plan cost = 0.005m + 46
Set new plan equal to current plan:
0.005m + 46 = 0.12m
Solve for [I]m[/I] in the equation 0.005m + 46 = 0.12m
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 0.005m and 0.12m. To do that, we subtract 0.12m from both sides
0.005m + 46 - 0.12m = 0.12m - 0.12m
[SIZE=5][B]Step 2: Cancel 0.12m on the right side:[/B][/SIZE]
-0.115m + 46 = 0
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 46 and 0. To do that, we subtract 46 from both sides
-0.115m + 46 - 46 = 0 - 46
[SIZE=5][B]Step 4: Cancel 46 on the left side:[/B][/SIZE]
-0.115m = -46
[SIZE=5][B]Step 5: Divide each side of the equation by -0.115[/B][/SIZE]
-0.115m/-0.115 = -46/-0.115
m = [B]400
She must talk over 400 minutes for the new plan to be a better deal
[URL='https://www.mathcelebrity.com/1unk.php?num=0.005m%2B46%3D0.12m&pl=Solve']Source[/URL][/B]

The planets in the solar system as set G

The planets in the solar system as set G.
Since Pluto was removed as a planet, we have the following set G with 8 elements:
G = [B]{Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}[/B]

The population of goats on a particular nature reserve t years after the initial population was sett

The population of goats on a particular nature reserve t years after the initial population was settled is modeled by p(t) = 4000 - 3000e^-0.2t. How many goats were initially present?
[U]Initially present means at time 0. Substituting t = 0, p(0), we get:[/U]
p(0) = 4000 - 3000e^-0.2(0)
p(0) = 4000 - 3000e^0
p(0) = 4000 - 3000(1)
p(0) = 4000 - 3000
[B]p(0) = 1000[/B]

The price p of a gym’s membership is $30 for an enrollment fee and $12 per week w to be a member. W

The price p of a gym’s membership is $30 for an enrollment fee and $12 per week w to be a member. What is the cost to be a member for 5 weeks?
Set up the cost function C(w)
C(w) = 12w + 30
The problem asks for C(5)
C(5) = 12(5) + 30
C(5) = 60 + 30
C(5) = [B]90[/B]

The principal randomly selected six students to take an aptitude test. Their scores were: 87.4 86.9

First, determine the [URL='http://www.mathcelebrity.com/statbasic.php?num1=87.4%2C86.9%2C89.9%2C78.3%2C75.1%2C70.6&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']mean and standard deviation[/URL] for the [I]sample[/I]
Mean = 81.3667
SD = 7.803
Next, use our [URL='http://www.mathcelebrity.com/normconf.php?n=6&xbar=81.3667&stdev=7.803&conf=90&rdig=4&pl=Small+Sample']confidence interval for the mean calculator[/URL] with these values and n = 6
[B]74.9478 < u < 87.7856[/B]

the product of 2 less than a number and 7 is 13

the product of 2 less than a number and 7 is 13
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 - 2 less than a number means we subtract 2 from x
x - 2
Part 3 - The phrase [I]product[/I] means we multiply x - 2 by 7
7(x - 2)
Part 4 - The phrase [I]is[/I] means an equation, so we set 7(x - 2) equal to 13
[B]7(x - 2) = 13[/B]

The product of a number b and 3 is no less than 12.

The product of a number b and 3 is no less than 12.
A number b is just written as b. So we have:
The product of b and 3 is no less than 12.
take this in parts:
[LIST]
[*]The product of b and 3: 3b
[*]The phrase [I]is no less than[/I] means an inequality, so we have greater than or equal to. We set 3b greater than or equal to 12
[/LIST]
[B]3b >= 12[/B]

the quotient of 3 and u is equal to 52 divided by u

the quotient of 3 and u is equal to 52 divided by u
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The quotient of 3 and u means we divide 3 by u: 3/u
[*]52 divided by u means we divide 52 by u: 52/u
[*]The phrase [I]is equal to[/I] means an equation, so we set (1) equal to (2)
[/LIST]
[B]3/u = 52/u[/B]

the quotient of 4 more than a number and 7 is 10

the quotient of 4 more than a number and 7 is 10
Take this algebraic expression in pieces:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
4 more than a number means we add 4 to x:
x + 4
The quotient of 4 more than a number and 7 means we divide x + 4 by 7
(x + 4)/7
The word [I]is[/I] means an equation, so we set (x + 4)/7 equal to 10
[B](x + 4)/7 = 10[/B]

the quotient of d and 182 is the same as w minus 137

The quotient of d and 182 is the same as w minus 137
Take this algebraic expression in 3 parts:
The quotient of d and 182
d/182
w minus 137
w - 137
The phrase [I]is the same as[/I] means we set d/182 equal to w - 137
[B]d/182 = w - 137[/B]

The quotient of t and 12 is the sum of s and r.

The quotient of t and 12 is the sum of s and r.
Step 1: The quotient of t and 12 is:
t/12
Step 2: The Sum of s and r is
s + r
Step 3: The word [I]is[/I] means equal to, so we set t/12 equal to s + r
[B]t/12 = s + r[/B]

the quotient of x and y is equal to the sum of a and b

the quotient of x and y is equal to the sum of a and b
The quotient of x and y:
x/y
The sum of a and b:
a + b
The phrase [I]is equal to[/I] means an equation, so we set x/y equal to a + b:
[B]x/y = a + b[/B]

The ratio of girls to boys is 14 girls to 12 boys. If there are 6 boys, how many girls are there?

The ratio of girls to boys is 14 girls to 12 boys. If there are 6 boys, how many girls are there?
Set up a proportion of girls to boys:
14/12 = g/6
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=14&num2=g&den1=12&den2=6&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL]:
[B]g = 7[/B]

The ratio of men to women working for a company is 3 to 4. If there are 81 men working for the compa

The ratio of men to women working for a company is 3 to 4. If there are 81 men working for the company, what is the total number of employees?
Men to women is 3:4. Set up a proportion where w is the number of women:
3/4 = 81/w
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=3&num2=81&den1=4&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get w = 108.
The problem asks for total employees, so we add men and women:
Total Employees = Men + Women
Total Employees = 81 + 108
Total Employees = [B]189[/B]

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5. If there were 4570 no votes, what was the total number of votes?
Set up a proportion where y is the number of yes votes to 4570 no votes
6/5 = y/4570
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=6&num2=y&den1=5&den2=4570&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
[B]y = 5484[/B]

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 4 to 3 . If there were 2958 no votes, what was the total number of votes?
Set up a ratio of yes to no votes
4/3 = x/2958
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=4&num2=x&den1=3&den2=2958&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get x = 3,944 for yes votes.
Adding yes votes and no votes together to get total votes, we get:
Total Votes = Yes Votes + No Votes
Total Votes = 3,944 + 2,958
Total Votes = [B]6,902[/B]

The sales price of a new compact disc player is $210 at a local discount store. At the store where t

The sales price of a new compact disc player is $210 at a local discount store. At the store where the sale is going on, each new cd is on sale for $11. If Kyle purchases a player and some cds for $243 how many cds did he purchase?
If Kyle bought the player, he has 243 - 210 = 33 left over.
Each cd is 11, so set up an equation to see how many CDs he bought:
11x = 33
Divide each side by 11
[B]x = 3[/B]

The scale of a map shows that 1/2 inch is equal to 3/4 of a mile. How many inches on a map would be

The scale of a map shows that 1/2 inch is equal to 3/4 of a mile. How many inches on a map would be equal to 3 miles?
Set up a proportion of scale to actual distance
1/2 / 3/4 = x/3
4/3 = x/3
Cross multiply:
3x = 12
Divide each side by 3:
3x/3 = 12/3
x = [B]4 (1/2 inch sections) or 2 inches[/B]

The scale on a map is 1 inch = 60 miles. If two cities are 75 miles apart, how far apart are they on

The scale on a map is 1 inch = 60 miles. If two cities are 75 miles apart, how far apart are they on the map?
Set up a proportion of inches to miles where n is the number of inches for 75 miles
1 inch/60 miles = n/75
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=1&num2=n&den1=60&den2=75&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
n = [B]1.25 inches[/B]

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for $40. Write a cost and revenue function and determine the break-even point.
[U]Calculate cost function C(b) with b as the number of books:[/U]
C(b) = Cost per book * b + Overhead
[B]C(b) = 15b + 5500[/B]
[U]Calculate Revenue Function R(b) with b as the number of books:[/U]
R(b) = Sales Price per book * b
[B]R(b) = 40b[/B]
[U]Calculate break even function E(b):[/U]
Break-even Point = Revenue - Cost
Break-even Point = R(b) - C(b)
Break-even Point = 40b - 15b - 5500
Break-even Point = 25b - 5500
[U]Calculate break even point:[/U]
Break-even point is where E(b) = 0. So we set 25b - 5500 equal to 0
25b - 5500 = 0
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-5500%3D0&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]b = 220[/B]

The science club charges 4.50 per car at their car wash. Write and solve and inequality to find how

The science club charges 4.50 per car at their car wash. Write and solve and inequality to find how many cars they have to wash to earn at least 300
Let x be the number of cars they wash. Set up our inequality. Note, at least 300 means 300 or greater, so we use greater than or equal to.
[U]Inequality:[/U]
[B]4.50x >= 300
[/B]
[U]So solve for x, divide each side by 4[/U]
[B]x >= 66.67[/B]

The set of all letters in the word p lus is

The set of all letters in the word p lus is
The cardinality of this set is 4 with the elements below:
[B]{p, l, u, s}[/B]

The set of all letters in the word true is

The set of all letters in the word true is:
We have [B]{t, r, u, e}[/B]

The set of all odd numbers between 10 and 30

The set of all odd numbers between 10 and 30
[B]{11, 13, 15, 17, 19, 21, 23, 25, 27, 29}[/B]

The set of months of a year ending with the letters “ber”.

The set of months of a year ending with the letters “ber”.
We build set S below:
[B]S = {September, October, November, December}[/B]
The cardinality of S, denoted |S|, is the number of items in S:
[B]|S| = 4[/B]

The set of months that contain less than 30 days

The set of months that contain less than 30 days.
Let M be the set. Only February has less than 30 days out of the 12 months.
[B]M = {February}[/B]

the set of natural numbers less than 7 that are divisible by 3

the set of natural numbers less than 7 that are divisible by 3
Natural Numbers less than 7
{1, 2, 3, 4, 5, 6}
Only 2 of them are divisible by 3. Divisible means the number is divided evenly, with no remainder:
[B]{3, 6}[/B]

The square of a number increased by 7 is 23

The square of a number increased by 7 is 23
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
[I]Increased by[/I] means we add 7 to x^2
x^2 + 7
The word [I]is[/I] means an equation. So we set x^2 + 7 equal to 23:
[B]x^2 + 7 = 23[/B]

The Square of a positive integer is equal to the sum of the integer and 12. Find the integer

The Square of a positive integer is equal to the sum of the integer and 12. Find the integer
Let the integer be x.
[LIST]
[*]The sum of the integer and 12 is written as x + 12.
[*]The square of a positive integer is written as x^2.
[/LIST]
We set these equal to each other:
x^2 = x + 12
Subtract x + 12 from each side:
x^2 - x - 12 = 0
We have a quadratic function. [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2-x-12%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Run it through our search engine[/URL] and we get x = 3 and x = -4.
The problem asks for a positive integer, so we have [B]x = 3[/B]

The sum is greater than 7, the sum is divisible by 2

The sum is greater than 7, the sum is divisible by 2
2 dice sum greater than 7 means 8, 9, 10, 11, 12.
Now take this set, and intersect it with sums divisible by 2.
[B]8, 10, 12[/B]

The sum of 2 times x and 5 times y is 7

The sum of 2 times x and 5 times y is 7
2 times x:
2x
5 times y:
5y
The sum of 2 times x and 5 times y:
2x + 5y
The word [I]is[/I] means equal to, so we set 2x + 5y equal to 7:
[B]2x + 5y = 7[/B]

the sum of 23 and victor age is 59

the sum of 23 and victor age is 59
Let's Victor's age be a.
The sum of 23 and Victor's age (a) mean we add a to 23:
23 + a
The word [I]is[/I] means an equation, so we set 23 + a equal to 59:
[B]23 + a = 59[/B] <-- This is our algebraic expression
Now if the problem asks you to take it a step further and solve this for a, [URL='https://www.mathcelebrity.com/1unk.php?num=23%2Ba%3D59&pl=Solve']we type this equation into our search engine[/URL] and we get:
[B]a = 36[/B]

the sum of 3 and 2x is 10

the sum of 3 and 2x is 10
The sum of 3 and 2x means we add 2x to 3:
3 + 2x
The word [I]is[/I] means an equation, so we set 3 + 2x equal to 10
[B]3 + 2x = 10[/B]

the sum of 6 and 7, plus 5 times a number, is -12

the sum of 6 and 7, plus 5 times a number, is -12
The sum of 6 and 7 means we add the two numbers:
6 + 7
This evaluates to 13
Next, we take 5 times a number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So we multiply x by 5:
5x
The first two words say [I]the sum[/I], so we add 13 and 5x
13 + 5x
The word [I]is[/I] means an equation, so we set 13 + 5x equal to -12
[B]13 + 5x = -12[/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=13%2B5x%3D-12&pl=Solve']type this algebraic expression into our search engine[/URL] and you get:
[B]x = -5[/B]

the sum of 7 times y and 3 is equal to 2

the sum of 7 times y and 3 is equal to 2
7 times y:
7y
The sum of 7 times y and 3 means we add 3 to 7y
7y + 3
The phrase [I]is equal to[/I] means an equation, so we set 7y + 3 equal to 2
[B]7y + 3 = 2[/B]

the sum of a and b minus 4 is 12

the sum of a and b minus 4 is 12
the sum of a and b
a + b
the sum of a and b minus 4
a + b - 4
The word [I]is[/I] means equal to, so we set a + b - 4 equal to 12:
a + b - 4 = 12

the sum of a number and 16 is e

A number means an arbitrary variable, let's call it x.
The sum of x and 16 means we add:
x + 16
Is, means equal to, so we set x + 16 = e
x + 16 = e

The sum of a number and 5 all divided by 2 is 17

The sum of a number and 5 all divided by 2 is 17
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The sum of a number and 5:
x + 5
All divided by 2:
(x + 5)/2
The word [I]is[/I] means equal to, so we set (x + 5)/2 equal to 17:
[B](x + 5)/2 = 17[/B]

the sum of a number and its reciprocal is 5/2

the sum of a number and its reciprocal is 5/2
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The reciprocal of the number means 1/x.
The sum means we add them:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 52
[B]x + 1/x = 52[/B]

The sum of a number and its reciprocal is 72

The sum of a number and its reciprocal is 72
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The reciprocal of the number is written as:
1/x
The sum of a number and its reciprocal means we add:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 72
[B]x + 1/x = 72[/B]

The sum of a number and its reciprocal is five.

The sum of a number and its reciprocal is five.
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The reciprocal of the number is 1/x.
The sum means we add them together:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 5
[B]x + 1/x = 5[/B]

The sum of a number and twice its reciprocal is 3

The sum of a number and twice its reciprocal is 3
the phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of a number means we take 1 over that number:
1/x
Twice the reciprocal means we multiply 1/x by 2:
2/x
The sum of a number and twice its reciprocal
x + 2/x
The word [I]is[/I] means equal to, so we set x + 2/x equal to 3
[B]x + 2/x = 3[/B]

the sum of a number divided by 8 and 3 equals 6

"A Number" means an arbitrary variable, let's call it x.
x divide d by 8 is written as a quotient
x/8
The sum of x/8 and 3 means we add:
x/8 + 3
Finally, equals means we have an equation, so we set our expression above equal to 6
x/8 + 3 = 6

the sum of a number times 3 and 30 is less than 17

the sum of a number times 3 and 30 is less than 17
A number is denoted as an arbitrary variable, let's call it x.
x
Times 3 means we multiply x by 3:
3x
The sum of a number times 3 and 30 means we add 30 to 3x above
3x + 30
Is less than 17 means we have an inequality, so we set 3x + 30 less than 17
3x + 30 < 17
To solve for x and see the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B30%3C17&pl=Solve']our calculator[/URL]:

the sum of doubling a number and 100 which totals to 160

the sum of doubling a number and 100 which totals to 160
Take this algebraic expression in pieces:
[LIST=1]
[*]Let the number be n.
[*]Double it, means we multiply n by 2: 2n
[*]The sum of this and 100 means we add 100 to 2n: 2n + 100
[*]The phrase [I]which totals[/I] means we set 2n + 100 equal to 160
[/LIST]
[B]2n + 100 = 160[/B] <-- This is our algebraic expression
If the question asks you to solve for n, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B100%3D160&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]n = 30[/B]

The sum of five and twice a number is 17

The sum of five and twice a number is 17
[U]The phrase a number means an arbitrary variable, let's call it x[/U]
x
[U]Twice a number means we multiply x by 2:[/U]
2x
[U]The sum of five and twice a number means we add 5 to 2x:[/U]
2x + 5
[U]The phrase [I]is[/I] means an equation, so we set 2x + 5 equal to 17 to get our algebraic expression[/U]
[B]2x + 5 = 17[/B]
[B][/B]
As a bonus, if the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D17&pl=Solve']type in this algebraic expression into our math engine[/URL] and we get:
x = 6

the sum of n and twice n is 12

Twice n means we multiply n by 2
2n
The sum of n and twice n means we add
n + 2n
The word [I]is[/I] means equal to, so we set that expression above equal to 12
n + 2n = 12
Combine like terms:
3n = 12
Divide each side of the equation by 3 to isolate n
n = 4
Check our work
Twice n is 2*4 = 8
Add that to n = 4
8 + 4
12

The sum of six times a number and 1 is equal to five times the number. Find the number.

The sum of six times a number and 1 is equal to five times the number. Find 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
the sum of six times a number and 1 is written as:
6x + 1
Five times the number is written as:
5x
The phrase [I]is equal to[/I] means an equation, so we set 6x + 1 equal to 5x:
6x + 1 = 5x
[URL='https://www.mathcelebrity.com/1unk.php?num=6x%2B1%3D5x&pl=Solve']Plugging this into our search engine[/URL], we get:
x = [B]-1[/B]

The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number

The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number by 18. What is the number?
Let x and (16-x) represent the original ten and units digits respectively
Reversing its digits increases the number by 18
Set up the relational equation
[10x + (16-x)] + 18 = 10(16 - x) + x
Solving for x
9x + 34 = 160 - 9x
Combine like terms
18x = 126
Divide each side of the equation by 18
18x/18 = 126/18
x = 7
So 16 - x = 16 - 7 = 9
The first number is 79, the other number is 97. and 97 - 79 = 18 so we match up.
The number in our answer is [B]79[/B]

The sum of the squares of c and d is 25

The sum of the squares of c and d is 25
The square of c means we we raise c to the power of 2:
c^2
The square of d means we we raise d to the power of 2:
d^2
The sum of the squares of c and d means we add d^2 to c^2:
c^2 + d^2
The word [I]is[/I] means equal to, so we set c^2 + d^2 equal to 25:
[B]c^2 + d^2 = 25[/B]

The sum of three consecutive integers is 42

Let the 3 integers be x, y, and z.
y = x + 1
z = y + 1, or x + 2.
Set up our equation:
x + (x + 1) + (x + 2) = 42
Group our variables and constants:
(x + x + x) + (1 + 2) = 42
3x + 3 = 42
Subtract 3 from each side:
3x = 39
Divide each side of the equation by 3:
[B]x = 13
So y = x + 1 = 14
z = x + 2 = 15
(x,y,z) = (13,14,15)[/B]

The Sum of three times a number and 18 is -39. Find the number

The Sum of three times a number and 18 is -39. Find the number.
A number means an arbitrary variable, let us call it x.
Three times x:
3x
The sum of this and 18:
3x + 18
Is means equal to, so we set 3x + 18 = -39
3x + 18 = -39
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']equation solver[/URL], we get [B]x = -19[/B]

The sum of twice an integer and 3 times the next consecutive integer is 48

The sum of twice an integer and 3 times the next consecutive integer is 48
Let the first integer be n
This means the next consecutive integer is n + 1
Twice an integer means we multiply n by 2:
2n
3 times the next consecutive integer means we multiply (n + 1) by 3
3(n + 1)
The sum of these is:
2n + 3(n + 1)
The word [I]is[/I] means equal to, so we set 2n + 3(n + 1) equal to 48:
2n + 3(n + 1) = 48
Solve for [I]n[/I] in the equation 2n + 3(n + 1) = 48
We first need to simplify the expression removing parentheses
Simplify 3(n + 1): Distribute the 3 to each term in (n+1)
3 * n = (3 * 1)n = 3n
3 * 1 = (3 * 1) = 3
Our Total expanded term is 3n + 3
Our updated term to work with is 2n + 3n + 3 = 48
We first need to simplify the expression removing parentheses
Our updated term to work with is 2n + 3n + 3 = 48
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(2 + 3)n = 5n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
5n + 3 = + 48
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 3 and 48. To do that, we subtract 3 from both sides
5n + 3 - 3 = 48 - 3
[SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE]
5n = 45
[SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE]
5n/5 = 45/5
Cancel the 5's on the left side and we get:
n = [B]9[/B]

The sum of two-fifths and f is one-half.

The sum of two-fifths and f is one-half.
We write two-fifths as 2/5.
The sum of two-fifths and f is written by adding f to two-fifths using the + sign:
2/5 + f
one-half is written as 1/2
The word [I]is[/I] means equals, so we set up an equation where 2/5 + f equal to 1/2
[B]2/5 + f = 1/2[/B]

the sum of x and 96 equals half of x

the sum of x and 96 equals half of x
half of x means we divide x by 2:
x/2
The sum of x and 96:
x + 96
The phrase equals means we set x + 96 equal to x/2:
[B]x + 96 = x/2[/B]

The sum of x and twice y is equal to m.

The sum of x and twice y is equal to m.
Twice y means we multiply y by 2:
2y
The sum of x and twice y:
x + 2y
The phrase [I]is equal to[/I] means an equation, so we set x + 2y equal to m
[B]x + 2y = m[/B]

The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your

The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equation that models the cost of each bracelet.
We set up a cost function as fixed cost plus total cost. Fixed cost is the shipping charge of $9. So we have the following cost function where n is the cost of the bracelets:
C(b) = nb + 9
We are given C(9) = 72 and b = 9
9n + 9 = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=9n%2B9%3D72&pl=Solve']Run this through our equation calculator[/URL], and we get [B]n = 7[/B].

The total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25

The total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25
Set up the cost function per x units:
[B]C(x) = 2900 + 25x[/B]

The total cost to fix your bike is $45 the parts cost $10 and the labor cost seven dollars per hour

The total cost to fix your bike is $45 the parts cost $10 and the labor cost seven dollars per hour how many hours were there:
Set up a cost function where h is the number of hours:
7h + 10 = 45
To solve for h, we t[URL='https://www.mathcelebrity.com/1unk.php?num=7h%2B10%3D45&pl=Solve']ype this equation into our search engine[/URL] and we get:
h = [B]5[/B]

the total of a and 352 equals a divided by 195

the total of a and 352 equals a divided by 195
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The total of a and 352 means we add 352 to a: a + 352
[*]a divided by 195: a/195
[*]The phrase [I]equals[/I] means we set (1) equal to (2) to get our final algebraic expression:
[/LIST]
[B]a + 352 = a/195[/B]

The value of a stock begins at $0.07 and increases by $0.02 each month. Enter an equation representi

The value of a stock begins at $0.07 and increases by $0.02 each month. Enter an equation representing the value of the stock v in any month m.
Set up our equation v(m):
[B]v(m) = 0.07 + 0.02m[/B]

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash t

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take?
Set up the earnings equation for the volleyball team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 4w + 81
Set up the earnings equation for the wrestling team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 2w + 85
If the raised the same amount in total, set both earnings equations equal to each other:
4w + 81 = 2w + 85
Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides
4w + 81 - 2w = 2w + 85 - 2w
[SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE]
2w + 81 = 85
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 81 and 85. To do that, we subtract 81 from both sides
2w + 81 - 81 = 85 - 81
[SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE]
2w = 4
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2w/2 = 4/2
w = [B]2 <-- How many cars it will take
[/B]
To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2:
E = 4(2) + 81
E = 8 + 81
E = [B]89 <-- Total Earnings[/B]

The world record for the mile in the year 1865 was held by Richard Webster of England when he comple

The world record for the mile in the year 1865 was held by Richard Webster of England when he completed a mile in 4 minutes and 36.5 seconds. The world record in 1999 was set by Hicham El Guerrouj when he ran a mile in 3 minutes and 43.13 seconds.
If both men ran the mile together, how many feet behind would Richard Webster be when Hichem El Guerrouj crossed the finish line?
Change times to seconds:
[LIST]
[*]4 minutes and 36.5 seconds = 4*60 + 36.5 = 240 + 36.5 = 276.5 seconds
[*]3 minute and 43.13 seconds = 3*60 + 43.13 = 180 + 43.13 = 223.13 seconds
[/LIST]
Now, find the distance Richard Webster travelled in 3 minutes and 43.13 seconds which is when Hiram El Guerrouj crossed the finish line.
1 mile = 5280 feet:
Set up a proportion of distance in feet to seconds where n is the distance Richard Webster travelled
5280/276.5 = n/223.13
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5280&num2=n&den1=276.5&den2=223.13&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
n = 4260.85 feet
Distance difference = 5280 - 4260.85 = [B]1019.15 feet[/B]

There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How

There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How many of each animal are there?
Chickens have 2 legs, pigs have 4 legs. Let c be the number of chickens and p be the number of pigs. Set up our givens:
(1) c + p = 13
(2) 2c + 4p = 40
[U]Rearrange (1) to solve for c by subtracting p from both sides:[/U]
(3) c = 13 - p
[U]Substitute (3) into (2)[/U]
2(13 - p) + 4p = 40
26 - 2p + 4p = 40
[U]Combine p terms[/U]
2p + 26 = 40
[U]Subtract 26 from each side:[/U]
2p = 14
[U]Divide each side by 2[/U]
[B]p = 7[/B]
[U]Substitute p = 7 into (3)[/U]
c = 13 - 7
[B]c = 6[/B]
For a shortcut, you could use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+p+%3D+13&term2=2c+%2B+4p+%3D+40&pl=Cramers+Method']simultaneous equations calculator[/URL]

There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?

There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?
We set up an equation to represent this:
5x + 3x = 144
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3x%3D144&pl=Solve']Typing this equation into our search engine[/URL], we get:
x = 18
This means we have:
Adults = 5(18)
[B]Adults = 90[/B]
Children = 3(18)
[B]Children = 54[/B]

There are 40 grams in 5 prunes. How much gram of weight is in 34 prunes

There are 40 grams in 5 prunes. How much gram of weight is in 34 prunes?
Set up a proportion of grams to prunes where g is the number of grams in 34 prunes:
40/5 = g/34
[URL='https://www.mathcelebrity.com/prop.php?num1=40&num2=g&den1=5&den2=34&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion of 40/5 = g/34 into our search engine[/URL], we get:
[B]g = 272[/B]

There are 4064 calories in 8 pints of strawberry icecream. How many calories are ther in each pint o

There are 4064 calories in 8 pints of strawberry ice cream. How many calories are there in each pint of strawberry ice cream?
Set up a proportion using x as the number of calories in 1 pint of ice cream.
4064/8 = x/1
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=4064&num2=x&den1=8&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
x = [B]508[/B]

There are 63 students in middle school chorus. There are 11 more boys than girls. How many boys x an

There are 63 students in middle school chorus. There are 11 more boys than girls. How many boys x and girls y are in the chorus?
Set up equations:
[LIST=1]
[*]x + y = 63
[*]x = y + 11
[/LIST]
Substitute (1) into (2)
y + 11 + y = 63
2y + 11 = 63
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=2y%2B11%3D63&pl=Solve']equation solver[/URL]:
[B]y = 26[/B]

There are 64 members in the history club. 11 less than half of the members are girls. How many membe

There are 64 members in the history club. 11 less than half of the members are girls. How many members are boys?
Set up two equations where b = the number of boys and g = the number of girls
[LIST=1]
[*]b + g = 64
[*]1/2(b + g) - 11 = g
[/LIST]
Substitute (1) for b + g into (2)
1/2(64) - 11 = g
32 - 11 = g
[B]g = 21[/B]
Substitute g = 21 into (1)
b + 21 = 64
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=b%2B21%3D64&pl=Solve']equation calculator[/URL], we get:
[B]b = 43[/B]

There are 76 milligrams of cholesterol in a 3.2 ounce serving of lobster. How much cholesterol is in

There are 76 milligrams of cholesterol in a 3.2 ounce serving of lobster. How much cholesterol is in a 6 ounce serving?
Let x equal the amount of cholesterol in milligrams for a 6 ounce service. Set up a proportion:
76/3.2 = x/6
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=76&num2=x&den1=3.2&den2=6&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] by plugging that expression into the search engine, we get x = 142.5

there are some red counters and some yellow counters in the ratio 1:5. There are 20 yellow counters

There are some red counters and some yellow counters in the ratio 1:5. There are 20 yellow counters in the bag.
Set up a proportion where x is the amount of red counters to 20 yellow counters
1/5 = x/20
Enter that in the search engine and our [URL='http://www.mathcelebrity.com/prop.php?num1=1&num2=x&den1=5&den2=20&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] gives us:
[B]x = 4[/B]

There is a ratio of 5 girls to 3 boys in the chorus. There are 24 boys in the chorus.How many girls

There is a ratio of 5 girls to 3 boys in the chorus. There are 24 boys in the chorus.How many girls are in the chorus?
Set up a proportion of girls to boys:
5/3 = g/24 where g is the number of girls for 24 boys.
Typing 5/3 = g/24 into the [URL='http://www.mathcelebrity.com/prop.php?num1=5&num2=g&den1=3&den2=24&propsign=%3D&pl=Calculate+missing+proportion+value']math tutoring calculator[/URL] gives us [B]g = 40[/B].

There were 150 students at a dance. There were 16 more boys than girls. How many boys were there?

Set up two equations:
(1) b = g + 16
(2) b + g = 150
Substitute equation (1) into (2)
(g + 16) + g = 150
Combine like terms
2g + 16 = 150
Subtract 16 from each side
2g = 134
Divide each side by 2 to isolate g
g = 67
Substitute this into equation (1)
b = 67 + 16
[B]b = 83[/B]

Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quo

Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be 20. What is the number
Let's call our number n.
Double the number means we multiply n by 2:
2n
Subtract 6 from the result means we subtract 6 from 2n:
2n - 6
Divide the answer by 2:
(2n - 6)/2
We can simplify this as n - 3
The quotient will be 20. This means the simplified term above is set equal to 20:
[B]n - 3 = 20 [/B] <-- This is our algebraic expression
If you want to take it a step further, and solve for n in the algebraic expression above, we [URL='https://www.mathcelebrity.com/1unk.php?num=n-3%3D20&pl=Solve']type this expression into our calculator[/URL], and get:
n = 23

Thirty is half of the sum of 4 and a number

Thirty is half of the sum of 4 and a number.
The phrase [I]a number[/I] represents an arbitrary variable, let's call it x.
The sum of 4 and a number:
4 + x
Half of this sum means we divide by 2:
(4 + x)/2
Set this equal to 30:
[B](4 + x)/2 = 30[/B] <-- This is our algebraic expression

Time and Distance

Let h be the number of hours that pass when Charlie starts. We have the following equations:
[LIST]
[*]Charlie: D = 40h + 9
[*]Danny: D = 55h
[/LIST]
Set them equal to each other:
40h + 9 = 55h
Subtract 40h from both sides:
15h = 9
h = 3/5
[B]3/5 of an hour = 3(60)/5 = 36 minutes[/B]

Time and Distance

Thank you so much
[QUOTE="math_celebrity, post: 1003, member: 1"]Let h be the number of hours that pass when Charlie starts. We have the following equations:
[LIST]
[*]Charlie: D = 40h + 9
[*]Danny: D = 55h
[/LIST]
Set them equal to each other:
40h + 9 = 55h
Subtract 40h from both sides:
15h = 9
h = 3/5
[B]3/5 of an hour = 3(60)/5 = 36 minutes[/B][/QUOTE]

Time Weighted Interest Method

Solves for Interest Rate based on 2 annual asset value events other than beginning or ending value using the Time Weighted Method

To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional po

To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional pound. To ship a package with FedEx, the cost will be $5 for the first pound and $0.30 for each additional pound. How many pounds will it take for UPS and FedEx to cost the same? If you needed to ship a package that weighs 8 lbs, which shipping company would you choose and how much would you pay?
[U]UPS: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.2(p - 1) + 7
[U]FedEx: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.3(p - 1) + 5
[U]When will the costs equal each other? Set the cost functions equal to each other:[/U]
0.2(p - 1) + 7 = 0.3(p - 1) + 5
0.2p - 0.2 + 7 = 0.3p - 0.3 + 5
0.2p + 6.8 = 0.3p + 4.7
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B6.8%3D0.3p%2B4.7&pl=Solve']type it in our search engine[/URL] and we get:
p = [B]21
So at 21 pounds, both UPS and FedEx costs are equal
[/B]
Now, find out which shipping company has a better rate at 8 pounds:
[U]UPS:[/U]
C(8) = 0.2(8 - 1) + 7
C(8) = 0.2(7) + 7
C(8) = 1.4 + 7
C(8) = 8.4
[U]FedEx:[/U]
C(8) = 0.3(8 - 1) + 5
C(8) = 0.3(7) + 5
C(8) = 2.1 + 5
C(8) = [B]7.1[/B]
[B]Therefore, FedEx is the better cost at 8 pounds since the cost is lower[/B]
[B][/B]

Today a car is valued at $42000. the value is expected to decrease at a rate of 8% each year. what i

Today a car is valued at $42000. the value is expected to decrease at a rate of 8% each year. what is the value of the car expected to be 6 years from now.
Depreciation at 8% per year means it retains (100% - 8%) = 92% of it's value. We set up our depreciation function D(t), where t is the number of years from right now.
D(t) = $42,000(0.92)^t
The problem asks for D(6):
D(6) = $42,000(0.92)^6
D(6) = $42,000(0.606355)
D(6) = [B]$25,466.91[/B]

Tom has a collection 21 CDs and Nita has a collection of 14 CDs. Tom is adding 3 cds a month to his

Tom has a collection 21 CDs and Nita has a collection of 14 CDs. Tom is adding 3 cds a month to his collection while Nita is adding 4 CDs a month to her collection. Find the number of months after which they will have the same number of CDs?
Set up growth equations for the CDs where c = number of cds after m months
Tom: c = 21 + 3m
Nita: c = 14 + 4m
Set the c equations equal to each other
21 + 3m = 14 + 4m
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=21%2B3m%3D14%2B4m&pl=Solve']equation calculator[/URL], we get [B]m = 7[/B]

Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli departm

Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli department at least 260 person-hours per week. Tom has one part-time employeewho works 20 hours per week. Each full-time employee works 40 hours per week. Write an inequality to determine n, the number of full-time employees Tom must schedule, so that his employees will work at least 260 person-hours per week.
Set up the inequality:
[LIST]
[*]Add the part-timer's hours of 20
[*]Full time hours is 40 times n employees
[*]At least means greater than or equal to, so we use the >= sign
[/LIST]
[B]40n + 20 >= 260[/B]

Translate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g to

Translate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g to represent Gregs age.
The sum of 17 and Greg's age:
g + 17
The word [I]is[/I] means equal to, so we set g + 17 equal to 43
[B]g + 17 = 43[/B] <-- This is our algebraic expression
If you want to solve this equation for g, use our [URL='http://www.mathcelebrity.com/1unk.php?num=g%2B17%3D43&pl=Solve']equation calculator[/URL].
[B]g = 26[/B]

Translate this sentence into an equation. 48 is the difference of Ritas age and 11 . Use the variabl

Translate this sentence into an equation. 48 is the difference of Ritas age and 11 . Use the variable r to represent Ritas age.
The difference of Rita's age and 11 is written:
r - 11
The phrase [I]is[/I] means equal to, so we set r - 11 equal to 48
r - 11 = 48

Translate this sentence into an equation. 49 is the difference of Diegos age and 17. Use the variabl

Translate this sentence into an equation. 49 is the difference of Diegos age and 17. Use the variable d to represent Diegos age.
The difference means we subtract, so we have d as Diego's age minus 17
d - 17
The word "is" means an equation, so we set d - 17 equal to 49
[B]d - 17 = 49[/B]

Trimmed Mean and Winsorized Mean

Given a number set and a trimmed mean percentage, this will calculate the trimmed mean (truncated mean) or winsorized mean.

triple the value of c plus 3 is 84

Triple the value of c means we multiply c by 3
3c
Plus 3 means we add 3
3c + 3
Is, means equal to, so we set our expression equal to 84
[B]3c +3 = 84
[/B]
If you want to solve that equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3c%2B3%3D84&pl=Solve']equation solver[/URL]:
c = 27

True False Equations

Determines if a set of addition and subtraction of numbers on each side of an equation are equivalent.
Also known as true or false equations

True or False (a) The normal distribution curve is always symmetric to its mean. (b) If the variance

True or False
(a) The normal distribution curve is always symmetric to its mean.
(b) If the variance from a data set is zero, then all the observations in this data set are identical.
(c) P(A AND A^{c})=1, where A^{c} is the complement of A.
(d) In a hypothesis testing, if the p-value is less than the significance level ?, we do not have sufficient evidence to reject the null hypothesis.
(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.
[B](a) True, it's a bell curve symmetric about the mean
(b) True, variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical
(c) True. P(A) is the probability of an event and P(Ac) is the complement of the event, or any event that is not A. So either A happens or it does not. It covers all possible events in a sample space.
(d) False, we have sufficient evidence to reject H0.
(e) False. Volume can be a decimal or fractional. There are multiple values between 127 and 128. So it's continuous.[/B]

Truth Tables

Sets up a truth table based on a logical statement of 1, 2 or 3 letters with statements such as propositions, equivalence, conjunction, disjunction, negation. Includes modus ponens.

twice the difference between x and 28 is 3 times a number

twice the difference between x and 28 is 3 times a number
The difference between x and 28:
x - 28
Twice the difference means we multiply x - 28 by 2:
2(x - 28)
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
3 times a number:
3x
The word [I]is[/I] means equal to, so we set 2(x - 28) equal to 3x:
[B]2(x - 28) = 3x[/B]

twice the difference of a number and 3 is equal to 3 times the sum of a number and 2

twice the difference of a number and 3 is equal to 3 times the sum of a number and 2.
We've got 2 algebraic expressions here. Let's take them in parts.
Left side algebraic expression: twice the difference of a number and 3
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]The word [I]difference[/I] means we subtract 3 from the variable x
[*]x - 3
[*]Twice this difference means we multiply (x - 3) by 2
[*]2(x - 3)
[/LIST]
Right side algebraic expression: 3 times the sum of a number and 2
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]The word [I]sum[/I] means we add 2 to the variable x
[*]x + 2
[*]3 times the sum means we multiply (x + 2) by 3
[*]3(x + 2)
[/LIST]
Now, we have both algebraic expressions, the problem says [I]is equal to[/I]
This means we have an equation, where we set the left side algebraic expression equal to the right side algebraic expression using the equal sign (=) to get our answer
[B]2(x - 3) = 3(x + 2)[/B]

twice the difference of a number and 55 is equal to 3 times the sum of a number and 8

twice the difference of a number and 55 is equal to 3 times the sum of a number and 8
Take this algebraic expression in pieces.
Left side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The difference of this number and 55 means we subtract 55 from x
x - 55
Twice the difference means we multiply x - 55 by 2
2(x - 55)
Right side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 8 means we add 8 to x
x + 8
3 times the sum means we multiply x + 8 by 3
3(x + 8)
Now that we have the left and right side of the expressions, we see the phrase [I]is equal to[/I]. This means an equation, so we set the left side equal to the right side:
[B]2(x - 55) = 3(x + 8)[/B]

twice the square root of a number increased by 5 is 23

twice the square root of a number increased by 5 is 23
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The square root of a number means we raise x to the 1/2 power:
sqrt(x)
the square root of a number increased by 5 means we add 5 to sqrt(x):
sqrt(x) + 5
twice the square root of a number increased by 5 means we multiply sqrt(x) + 5 by 2:
2(sqrt(x) + 5)
The phrase [I]is 23[/I] means we set 2(sqrt(x) + 5) equal to 23:
[B]2(sqrt(x) + 5) = 23[/B]

twice the sum of a and b is thrice c

twice the sum of a and b is thrice c
The sum of a and b:
a + b
twice the sum of a and b means we multiply the sum of a and b by 2:
2(a + b)
Thrice c means we multiply c by 3:
3c
The word [I]is[/I] means equal to, so we set 2(a + b) equal to 3c:
[B]2(a + b) = 3c[/B]

Twice x increased by the cube of y equals z

Twice x increased by the cube of y equals z
[LIST]
[*]Twice x means we multiply x by 2: 2x
[*]Increased this by the cube of y which is y^3. So we have 2x + y^3
[*]Now, we set this entire expression equal to z: 2x + y^3 = z
[/LIST]

Two dice are rolled. Enter the size of the set that corresponds to the event that both dice are odd.

Two dice are rolled. Enter the size of the set that corresponds to the event that both dice are odd.
If dice 1 is odd, then we have the following face values:
{1, 3, 5}
If dice 2 is odd, then we have the following face values:
{1, 3, 5}
[URL='https://www.mathcelebrity.com/2dice.php?gl=1&opdice=1&pl=Both+Odd&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']From this 2 dice odds face link[/URL], we see that the size of the set is 9.
[LIST=1]
[*]{1, 1}
[*]{1, 3}
[*]{1, 5}
[*]{3, 1}
[*]{3, 3}
[*]{3, 5}
[*]{5, 1}
[*]{5, 3}
[*]{5, 5}
[/LIST]

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worke

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of 1225. what was the rate charged per hour by each mechanic if the sum of the two rates was 170 per hour?
Set up two equations:
(1) 10x + 5y = 1225
(2) x + y = 170
Rearrange (2)
x = 170 - y
Substitute that into (1)
10(170 - y) + 5y = 1225
1700 - 10y + 5y = 1225
1700 - 5y = 1225
Move 5y to the other side
5y + 1225 = 1700
Subtract 1225 from each side
5y =475
Divide each side by 5
[B]y = 95[/B]
Which means x = 170 - 95, [B]x = 75[/B]

Two mechanics worked on a car. the first mechanic worked for 5 hours snd the second mechanic worked

Two mechanics worked on a car. the first mechanic worked for 5 hours snd the second mechanic worked for 15 hours. Together they charged a total of $2375. What was the rate charged per hour by each mechanic if the sum of the two rates was $235 per hour?
Setup equations where x is the rate of the first mechanic and y is the rate of the second mechanic:
[LIST]
[*]5x + 15y = 2375
[*]x + y = 235
[/LIST]
Using Cramers method with our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=5x+%2B+15y+%3D+2375&term2=x+%2B+y+%3D+235&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[LIST]
[*][B]x = 115[/B]
[*][B]y = 120[/B]
[/LIST]

two numbers have an average of 2100 and one number is $425 more than the other number. What are the

two numbers have an average of 2100 and one number is $425 more than the other number. What are the numbers
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*](x + y)/2 = 2100 (Average)
[*]y = x + 425
[/LIST]
Rearrange equation (1) by cross multiplying
x + y = 2 * 2100
x + y = 4200
So we have our revised set of equations:
[LIST=1]
[*]x + y = 4200
[*]y = x + 425
[/LIST]
Substituting equation (2) into equation (1) for y, we get:
x + (x + 425) = 4200
Combining like terms, we get:
2x + 425 = 4200
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B425%3D4200&pl=Solve']equation solver[/URL], we get:
x = [B]1887.5[/B]
Which means using equation (2), we get
y = 1887.5 + 425
y = [B]2312.5[/B]

Two numbers total 83 and have a difference of 17 find the two numbers

Let the numbers be x and y. Set up our givens:
[LIST=1]
[*]x + y = 83
[*]x - y = 17
[*]Rearrange (2), by adding y to each side, we have: x = 17 + y
[/LIST]
[U]Substitute (3) into (1):[/U]
(17 + y) + y = 83
[U]Group y terms[/U]
2y + 17 = 83
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2y%2B17%3D83&pl=Solve']equation solver[/URL], we get:[/U]
[B]y = 33
[/B]
[U]Substitute that into (3)[/U]
x = 17 + 33
[B]x = 50
[/B]
So our two numbers (x, y) = (33, 50)

u and 201 more equals q

201 more means we add:
u + 201
We set that expression equal to q
u + 201 = q

u cubed equals nine

u cubed equals nine
u cubed means we raise u to the 3rd power:
u^3
We set this equal to 9:
[B]u^3 = 9[/B]

Units of Output (Service Output) Depreciation

Given an asset value, salvage value, production units, and units per period, this calculates the depreciation per period using the units of output depreciation (service output depreciation)

Utility and Cost Utility Ratio

Given 2 methods with a set of utilities and weights/probabilities, this will calculate the utility for each method, as well as the total utility using the additive method, as well as the Cost Utility Ratio

v equals 66 decreased by d

66 decreased by d means we subtract:
66 - d
v equals means we set our entire expression equal to v
[B]66 - d = v[/B]

v is equal to the product of 7 and the sum of u and 6

v is equal to the product of 7 and the sum of u and 6
[LIST]
[*]Sum of u and 6: u + 6
[*]the product of 7 and the sum of u and 6: 7(u + 6)
[*]We set this expression equal to v:
[/LIST]
[B]v = 7(u + 6)[/B]

Video store movie rental plans. Plan A 25 membership fee plus 1.25 for movie. Plan B 40 for unlimite

Video store movie rental plans. Plan A 25 membership fee plus 1.25 for movie. Plan B 40 for unlimited rentals. What number of movies rentals is plan B less than plan A?
Let x equal the number of movies rented and C the cost for rentals
Plan A: C = 1.25x + 25
Plan B: C = 40
Set up the inequality:
1.25x + 25 > 40
Subtract 25 from each side:
1.25x > 15
Divide each side of the inequality by 1.25
x > 12
So [B]13[/B] rentals or more make Plan B less than Plan A.

Volatility

Given a set of stock prices, this determines expected rates of return and volatility

Water flows from tank A to tank B at the rate of 2 litres per minute.

[QUOTE="Jahn, post: 78, member: 5"]Water flows from tank A to tank B at the rate of 2 litres per minute. Initially tank A has 200 litres in it and tank B has 100 Litres in it. Water drains from tank B at 0.5 litres per minute.
After how many minutes are there equal volumes of water in the 2 tanks?
Write an equation and solve it.[/QUOTE]
Tank A: V = 200 - 2x
Tank B: V = 100 - 0.5x
Where x is the number of minutes passed.
Set them equal to each other
200 - 2x = 100 - 0.5x
Subtract 100 from each side:
100 - 2x = -0.5x
Add 2x to each side:
1.5x = 100
Divide each side of the equation by x:
x = 66.66666667

Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM)

Calculates the Weighted Average Cost of Capital (WACC) and also calculates the return on equity if not given using the Capital Asset Pricing Model (CAPM) using debt and other inputs such as Beta and risk free rate.

Wendy is paid $7.50 per hour plus a bonus of $80 each week. Last week Wendy earned $312.50. How many

Wendy is paid $7.50 per hour plus a bonus of $80 each week. Last week Wendy earned $312.50. How many hours did Wendy work last week?
Setup the earnings equation with h hours:
7.5h + 80 = 312.50
Solve for [I]h[/I] in the equation 7.5h + 80 = 312.50
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 80 and 312.50. To do that, we subtract 80 from both sides
7.5h + 80 - 80 = 312.50 - 80
[SIZE=5][B]Step 2: Cancel 80 on the left side:[/B][/SIZE]
7.5h = 232.5
[SIZE=5][B]Step 3: Divide each side of the equation by 7.5[/B][/SIZE]
7.5h/7.5 = 232.5/7.5
h = [B]31
[URL='https://www.mathcelebrity.com/1unk.php?num=7.5h%2B80%3D312.50&pl=Solve']Source[/URL][/B]

what is a well defined set

what is a well defined set?
A well defined set is with no ambiguity or confusion about what belongs to the set. Think of it as a collection of distinct objects:
Examples:
[LIST]
[*]Set of the first 5 even numbers: {2, 4, 6, 8, 10}
[*]Set of weekend days: {Saturday, Sunday}
[/LIST]

What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.4%? Round

What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.4%? Round to three decimal places. Use a 365 day year.
[U]Set up the accumulation equation:[/U]
(1+i)^365 = 1.054
[U]Take the natural log of each side[/U]
365 * Ln(1 + i) = 1.054
Ln(1 + i) = 0.000144089
[U]Use each side as a exponent to eulers constant e[/U]
(1 + i) = e^0.000144089
1 + i = 1.000144099
i = 0.000144099 or [B].0144099%[/B]

What is the sample space for a 10 sided die?

What is the sample space for a 10 sided die?
Sample space means the set of all possible outcomes. For a 10-sided die, we have:
[B]{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}[/B]

WHAT SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512

WHAT SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512
We set up an arbitrary number x.
Subtracted from is written as
-9876 - x
The phrase [I]to obtain[/I] means an equation, so we set -9876 - x equal to -9512
-9876 - x = -9512
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=-9876-x%3D-9512&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]364[/B]

When 20 is subtracted from 3 times a certain number, the result is 43

A certain number means an arbitrary variable, let's call it x
x
3 times x
3x
20 is subtracted from 3 time x
3x - 20
The result is means equal to, so we set 3x - 20 equal to 43 for our algebraic expression
[B]3x - 20 = 43
[/B]
If you need to solve this, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-20%3D43&pl=Solve']equation calculator[/URL]:
[B]x = 21[/B]

When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negati

When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negative solution.
Let the number be n.
Square of a number:
n^2
28 is subtracted from the square of a number:
n^2 - 28
3 times the number:
3n
[I]The result is[/I] mean an equation, so we set n^2 - 28 = 3n
n^2 - 28 = 3n
Subtract 3n from each side:
n^2 - 3n - 28 = 3n - 3n
The right side cancels to 0, so we have:
n^2 - 3n - 28 = 0
This is a quadratic equation in standard form, so we [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-3n-28%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']use our quadratic calculator[/URL] to solve:
We get two solutions for n:
n = (-4, 7)
The question asks for the negative solution, so our answer is:
[B]n = -4[/B]

When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unkn

When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unknown number. Write the translated equation below.
[LIST=1]
[*]39 added to a number is written as n + 39
[*]40 times the number is written as 40n
[*]The result is means we have an equation, so set (1) equal to (2)
[/LIST]
n+ 39 = 40n
Running [URL='http://www.mathcelebrity.com/1unk.php?num=n%2B39%3D40n&pl=Solve']n + 39 = 40n through the search engine[/URL], we get[B] n = 1[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the num

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. Find the number
The phrase [I]a number, [/I]means an arbitrary variable, let's call it "x".
4 times a number, increased by 40, means we multiply 4 times x, and then add 40
4x + 40
100 decreased by the number means we subtract x from 100
100 - x
The problem tells us both of these expressions are the same, so we set them equal to each other:
4x + 40 = 100 - x
Add x to each side:
4x + x + 40 = 100 - x + x
The x's cancel on the right side, so we have:
5x + 40 = 100
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B40%3D100&pl=Solve']Typing this equation into the search engine[/URL], we get [B]x = 12[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the num

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
4 times a number means we multiply x by 4:
4x
Increased by 40 means we add 40 to 4x:
4x + 40
100 decreased by the number means we subtract x from 100:
100 - x
The phrase [I]is the same as[/I] means equal to, so we set 4x + 40 equal to 100 - x
4x + 40 = 100 - x
Solve for [I]x[/I] in the equation 4x + 40 = 100 - x
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4x and -x. To do that, we add x to both sides
4x + 40 + x = -x + 100 + x
[SIZE=5][B]Step 2: Cancel -x on the right side:[/B][/SIZE]
5x + 40 = 100
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 40 and 100. To do that, we subtract 40 from both sides
5x + 40 - 40 = 100 - 40
[SIZE=5][B]Step 4: Cancel 40 on the left side:[/B][/SIZE]
5x = 60
[SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE]
5x/5 = 60/5
x = [B]12[/B]
Check our work for x = 12:
4(12) + 40 ? 100 - 12
48 + 40 ? 100 - 12
88 = 88

When 54 is subtracted from the square of a number, the result is 3 times the number.

When 54 is subtracted from the square of a number, the result is 3 times the number.
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
Square the number, means raise it to the 2nd power:
x^2
Subtract 54:
x^2 - 54
The phrase [I]the result[/I] means an equation, so we set x^2 - 54 equal to 3
[B]x^2 - 54 = 3[/B]

When 9 is subtracted from 5 times a number ,the result is 31

When 9 is subtracted from 5 times a number ,the result is 31
A number means an arbitrary variable, let's call it x.
5 times this number is written as 5x.
9 subtracted from this is written as 5x - 9
[I]The result[/I] means we have an equation, so we set [B]5x - 9 = 31[/B]. This is our algebraic expression.
Now if we want to solve for x, we [URL='http://www.mathcelebrity.com/1unk.php?num=5x-9%3D31&pl=Solve']plug this equation into the search engine [/URL]and get [B]x = 8[/B].

When a dog noticed a fox, they were 60 meters apart. The dog immediately started to chase the fox at

When a dog noticed a fox, they were 60 meters apart. The dog immediately started to chase the fox at a speed of 750 meters per minute. The fox started to run away at a speed of 720 meters per minute. How soon will the dog catch the fox?
The dog sits a position p.
Distance = Rate x Time
The dogs distance in minutes is D = 720t
The fox sits at position p + 60
Distance = Rate x Time
The fox's distance in minutes is D = 750t - 60 <-- Subtract 60 since the fox is already ahead 60 meters.
We want to know when their distance (location) is the same. So we set both distance equations equal to each other:
720t = 750t - 60
[URL='https://www.mathcelebrity.com/1unk.php?num=720t%3D750t-60&pl=Solve']Using our equation calculator[/URL], we get [B]t = 2[/B].
Let's check our work:
Dog's distance is 720(2) = 1440
Fox's distance is 750(2) - 60 = 1,440

When the drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened, it tak

When the drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened, it takes 5 hours to empty the pool. The pool is being filled, but the drain was accidentally left open. How long until the pool is completely filled?
Set up unit fill rates per hour:
[LIST]
[*]1/4 of the pool is filled each hour
[*]1/5 of the pool is drained away each hour
[/LIST]
The amount left over after an hour of filling minus draining is:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Subtract']1/4 - 1/5[/URL] = 1/20
Therefore, it take [B]20 hours to fill the pool[/B]

When the side of a square is doubled in length, its area increases by 432 square inches. What is the

When the side of a square is doubled in length, its area increases by 432 square inches. What is the size of the original square?
Original square side length is s
Area = s^2
Double the side lengths to 2s
New area = (2s)^2 = 4s^2
Setup the difference relation:
4s^2 - s^2 = 432
3s^2 = 432
Divide each side by 3:
3s^2/3 = 432/3
s^2 = 144
s = [B]12[/B]

When twice a number is reduced by 15 you get 95 what is the number

When twice a number is reduced by 15 you get 95 what is the number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
[I]Twice[/I] x means we multiply x by 2
2x
[I]Reduced by[/I] 15 means we subtract 15
2x - 15
[I]You get[/I] means equal to, as in an equation. Set 2x - 15 = 95
2x - 15 = 95 <-- This is our algebraic expression.
[URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D95&pl=Solve']Type 2x - 15 = 95 into the search engine[/URL] and we get [B]x = 55[/B].

Whole Numbers

Shows a set amount of whole numbers and cumulative sum

Write a system of equations to describe the situation below, solve using any method, and fill in the

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Hugo is going to send some flowers to his wife. Somerville Florist charges $2 per rose, plus $39 for the vase. Dwaynes Flowers, in contrast, charges $3 per rose and $10 for the vase. If Hugo orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be? How many roses would there be?
Let r be the number of roses and C(r) be the cost function. The vase is a one-time cost.
Somerville Florist:
C(r) = 2r + 39
Dwaynes Flowers
C(r) = 3r + 10
Set them equal to each other:
2r + 39 = 3r + 10
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2r%2B39%3D3r%2B10&pl=Solve']equation calculator[/URL], we get:
[B]r = 29[/B]

Write in set builder form {all possible numbers formed by any two of the digits 1 2 5}

Write in set builder form {all possible numbers formed by any two of the digits 1 2 5}
With 3 numbers, we got [URL='https://www.mathcelebrity.com/factorial.php?num=3!&pl=Calculate+factorial']3! = 6[/URL] possible numbers formed by the two digits
[LIST=1]
[*]12
[*]15
[*]21
[*]25
[*]51
[*]52
[/LIST]
In set builder notation, we write this as:
{x : x ? {12, 15, 21, 25, 51, 52})
x such that x is a element of the set {12, 15, 21, 25, 51, 52}

Write the interval (2,5) in set builder notation

Write the interval (2,5) in set builder notation
It's a closed interval, so [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=%5B2%2C5%5D&pl=Show+Interval+Notation']we type in [2,5] into the search engine[/URL], and we get:
[B]{x|2<= x <= 5}[/B]

Write the sentence as an equation. 19 is equal to c less than 321

Write the sentence as an equation. 19 is equal to c less than 321
c less than 321:
321 - c
The phrase [I]is equal to[/I] means an equation, so we set 321 - c equal to 19:
[B]321 - c = 19[/B]

writing and solving equations

Your answer is correct.
Here is how I set up the profit equation where h is the hours worked and x is the supply cost:
P(h) = 15.35h + x
We know P(4) = 141.73
P(4) = 15.35(4) + x
141.73 = 15.35(4) + x
Simplify
141.73 = 61.4 + x
Subtract 61.4 from each side:
[B]x = 80.33[/B]

x is a multiple of 6 and 1 ? x ? 16

x is a multiple of 6 and 1 ? x ? 16.
We want multiples of 6 between 1 and 16.
We start with 6.
Another multiple of 6 is 12
The next multiple of 6 is 18, which is out side the range of 1 ? x ? 16.
So our number set is [B]x = {6, 12}[/B]

x is a woman who served as US president before 2000

x is a woman who served as US president before 2000
No woman US presidents before 2000, so we have the empty set.
[B]x = {}[/B]

X plus 9 is equal to 3 times x minus 4

X plus 9 is equal to 3 times x minus 4
x plus 9:
x + 9
3 times x minus 4:
3x - 4
The phrase [I]is equal to[/I] means an equation, so we set x + 9 equal to 3x - 4:
[B]x + 9 = 3x - 4[/B]

X to the 9th is less than or equal to 38

X to the 9th is less than or equal to 38:
x to the 9th means 9th power:
x^9
We set this less than or equal 38:
[B]x^9 <= 38[/B]

x tripled less two is 5

x tripled less two is 5
x tripled means we multiply x by 3
3x
Less two means we subtract 2 from 3x
3x - 2
[I]Is[/I] means equal to, so we set 3x - 2 equal to 5
[B]3x - 2 = 5[/B]
[B][/B]
To solve this equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-2%3D5&pl=Solve']equation solver[/URL].

y is the sum of twice a number and 3

y is the sum of twice a number and 3
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
twice a number means we multiply x by 2:
2x
the sum of twice a number and 3:
2x + 3
The word [I]is[/I] means equal to, so we set 2x + 3 equal to y
[B]y = 2x + 3[/B]

y minus 10 is equal to the product of y and 8

y minus 10 is equal to the product of y and 8.
Take this algebraic expression in 3 parts:
Part 1: y minus 10
Subtract 10 from the variable y
y - 10
Part 2: The product of y and 8
We multiply 8 by the variable y
8y
Part 3: The phrase [I]is equal to[/I] means an equation, so we set y - 10 equal to 8y
[B]y - 10 = 8y[/B]

You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $1

You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $15 each and you paid $6.50 a piece plus a $50 set-up fee and $25 for shipping. How many shirts do you have to sell to break even? Round to the nearest whole number.
[U]Step 1: Calculate Your Cost Function C(s) where s is the number of t-shirts[/U]
C(s) = Cost per Shirt * (s) Shirts + Set-up Fee + Shipping
C(s) = $6.50s + $50 + $25
C(s) = $6.50s + 75
[U]Step 2: Calculate Your Revenue Function R(s) where s is the number of t-shirts[/U]
R(s) = Price Per Shirt * (s) Shirts
R(s) = $15s
[U]Step 3: Calculate Break-Even Point[/U]
Break Even is where Cost = Revenue. Set C(s) = R(s)
$6.50s + 75 = $15s
[U]Step 4: Subtract 6.5s from each side[/U]
8.50s = 75
[U]Step 5: Solve for s[/U]
[URL='https://www.mathcelebrity.com/1unk.php?num=8.50s%3D75&pl=Solve']Run this through our equation calculator[/URL] to get s = 8.824. We round up to the next integer to get [B]s = 9[/B].
[B][URL='https://www.facebook.com/MathCelebrity/videos/10156751976078291/']FB Live Session[/URL][/B]

You and your friend are playing a number-guessing game. You ask your friend to think of a positive n

You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen?
Let n be our original number.
Square the number means we raise n to the power of 2:
n^2
Multiply the result by 2:
2n^2
And then add three:
2n^2 + 3
If the friend's final answer is 53, this means we set 2n^2 + 3 equal to 53:
2n^2 + 3 = 53
To solve for n, we subtract 3 from each side, to isolate the n term:
2n^2 + 3 - 3 = 53 - 3
Cancel the 3's on the left side, and we get:
2n^2 = 50
Divide each side of the equation by 2:
2n^2/2 = 50/2
Cancel the 2's, we get:
n^2 = 25
Take the square root of 25
n = +-sqrt(25)
n = +-5
We are told the number is positive, so we discard the negative square root and get:
n = [B]5[/B]

You and your friend are saving for a vacation. You start with the same amount and save for the same

You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save 75 per week, and your friend saves 50 per week. When vacation time comes, you have 950, and your friend has 800. How much did you start with, and for how many weeks did you save?
[U]Let w be the number of weeks. Set up two equations where s is the starting amount:[/U]
(1) s + 75w =950
(2) s + 50w = 800
[U]Rearrange (1) into (3) to solve for s by subtracting 75w[/U]
(3) s = 950 - 75w
[U]Rearrange (2) into (4) to solve for s by subtracting 50w[/U]
(4) s = 800 - 50w
[U]Set (3) and (4) equal to each other so solve for w[/U]
950 - 75w = 800 - 50w
[U]Add 75w to each side, and subtract 950 from each side:[/U]
25w = 150
[U]Divide each side by w[/U]
[B]w = 6[/B]
Now plug w = 6 into (3)
s = 950 - 75(6)
s = 950 - 450
[B]s = 500[/B]

You are baking muffins for your class. There are 17 total students in your class and you have baked

You are baking muffins for your class. There are 17 total students in your class and you have baked 5 muffins. Write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. Write your equation so that the units on each side of the equation are muffins per student.
[U]Calculate total muffins:[/U]
Total muffins = 2 muffins per student * 17 students
Total muffins = 34
[U]Set up the equation using x for muffins:[/U]
[B]x + 5 = 34
[/B]
[U]To Solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B5%3D34&pl=Solve']type it in our search engine[/URL] and we get:[/U]
x = [B]29
[/B]

You are comparing the costs of producing shoes at two different manufacturers. Company 1 charges $5

You are comparing the costs of producing shoes at two different manufacturers. Company 1 charges $5 per pair of shoes plus a $650 flat fee. Company 2 charges $4 per pair of shoes plus a $700 flat fee. How many pairs of shoes are produced when the total costs for both companies are equal?
Let s be the number of shoes. We have two equations:
(1) C = 5s + 650
(2) C = 4s + 700
Set the costs equal to each other
5s + 650 = 4s + 700
Subtract 4s from each side
s + 650 = 700
Subtract 650 from each side
[B]s =50[/B]

You are heading to Cedar Point for the day. It costs $50 to get in to the park and each ride costs $

You are heading to Cedar Point for the day. It costs $50 to get in to the park and each ride costs $2 for a ticket. Write an expression for the total cost of going to Cedar Point where r is the number of rides.
Set up the cost equation C(r):
C(r) = Cost per ride * r rides + Park Fee
[B]C(r) = 2r + 50[/B]

You are offered two different sales jobs. The first company offers a straight commission of 6% of th

You are offered two different sales jobs. The first company offers a straight commission of 6% of the sales. The second company offers a salary of $330 per week plus 2% of the sales. How much would you have to sell in a week in order for the straight commission offer to be at least as good?
Let s be the sales and C be the weekly commission for each sales job. We have the following equations:
[LIST=1]
[*]C = 0.06s
[*]C = 330 + 0.02s
[/LIST]
Set them equal to each other:
0.06s = 330 + 0.02s
Subtract 0.02s from each side:
0.04s = 330
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.04s%3D330&pl=Solve']equation solver[/URL], we get [B]s = 8,250[/B]

You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet.

You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet. Company A charges $2.99 per square foot plus a $200 installation charge. Company B charges $19.99 per square yard plus a $500 installation charge. What is the best deal?
Did you notice the word snuck in on this problem? Company B is given in square [I][B]yards[/B][/I], not feet. Let's convert their price to square feet to match company A.
[U]Company B conversion:[/U]
Since we have 1 square yard = 3 feet * 3 feet = 9 square feet, we need to solve the following proportion:
$19.99/square yard * 1 square yard/9 feet = $19.99 square yard / 9 feet = $2.22 / square foot.
Now, let's set up the cost equations C(s) for each Company in square feet (s)
[LIST]
[*]Company A: C(s) = 200 + 2.99s
[*]Company B: C(s) = 500 + 2.22s
[/LIST]
The problem asks for s = 30 feet * 50 feet = 1500 square feet. So we want to calculate C(1500)
[U]Company A:[/U]
C(1500) = 200 + 2.99(1500)
C(1500) = 200 + 4485
C(1500) = 4685
[U]Company B:[/U]
C(1500) = 500 + 2.22(1500)
C(1500) = 500 + 3330
C(1500) = 3830
Since [B]Company B[/B] has the lower cost per square foot, they are the better buy.

You are using a spinner with the numbers 1-10 on it. Find the probability that the pointer will sto

You are using a spinner with the numbers 1-10 on it. Find the probability that the pointer will stop on an odd number or a number less than 4.
We want P(odd number) or P(n<4).
[LIST]
[*]Odd numbers are {1, 3, 5, 7, 9}
[*]n < 4 is {1, 2, 3}
[/LIST]
We want the union of these 2 sets:
{1, 2, 3, 5, 7, 9}
We have 6 possible pointers in a set of 10.
[B]6/10 = 3/5 = 0.6 or 60%[/B]

You can afford monthly deposits of $270 into an account that pays 3.0% compounded monthly. How long

You can afford monthly deposits of $270 into an account that pays 3.0% compounded monthly. How long will it be until you have $11,100 to buy a boat. Round to the next higher month.
[U]Set up our accumulation expression:[/U]
270(1.03)^n = 11100
1.03^n = 41.1111111
[U]Take the natural log of both sides[/U]
n * Ln(1.03) = 41.1111111
n = 3.71627843/0.0295588
n = 125.72 so round up to [B]126[/B]

You can buy 8 DVDs for $48,how many can you buy for 96$

Set up a proportion:
8/48 = x/96
Plug this into our [URL='http://www.mathcelebrity.com/prop.php?num1=8&num2=x&den1=48&den2=96&propsign=%3D&pl=Calculate+missing+proportion+value']calculator[/URL]:
You get x = 16.

You can get 2 different moving companies to help you move. The first one charges $150 up front then

You can get 2 different moving companies to help you move. The first one charges $150 up front then $38 an hour. The second one charges $230 then $30 an hour, at what exact time will Both companies cost the same
[U]Company 1: We set up the cost equation C(h) where h is the number of hours[/U]
C(h) = Hourly Rate * h + up front charge
C(h) = 38h + 150
[U]Company 2: We set up the cost equation C(h) where h is the number of hours[/U]
C(h) = Hourly Rate * h + up front charge
C(h) = 30h + 230
The question asks for h when both cost equations C(h) are equal. So we set both C(h) equations equal to other:
38h + 150 = 30h + 230
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=38h%2B150%3D30h%2B230&pl=Solve']type this equation into our search engine [/URL]and we get:
h = [B]10[/B]

You can pay a daily entrance fee of $3 or purchase a membership for the 12 week summer season for $8

You can pay a daily entrance fee of $3 or purchase a membership for the 12 week summer season for $82 and pay only $1 per day to swim. How many days would you have to swim to make the membership worthwhile?
Set up cost equations:
Daily entrance fee:
3d where d is the number of days of membership
Membership fee
82 + 1d
Set them equal to each other
82 + 1d = 3d
Subtract d from each side:
2d = 82
Divide each side by 2
[B]d = 41[/B]

You have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account a

You have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account and saves $19 per week. How many weeks will it take for you and your friend to have the same balance?
[U]Set up the savings account S(w) for you where w is the number of weeks[/U]
S(w) = 140 + 10w
[U]Set up the savings account S(w) for your friend where w is the number of weeks[/U]
S(w) = 95 + 19w
The problem asks for the number of weeks (w) when the balances are the same. So set both equations equal to each other:
140 + 10w = 95 + 19w
To solve this equation for w, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2B10w%3D95%2B19w&pl=Solve']we type it in the search engine[/URL] and get:
w = [B]5[/B]

You have $37 to plant garden. If you spend $12.25 on seeds, how many packs of vegetable plants can

You have $37 to plant garden. If you spend $12.25 on seeds, how many packs of vegetable plants can you buy for 2.75 each?
[U]How much do we have to spend on plants?[/U]
$37 - 12.25 = $24.75
[U]Calculate how many vegetable plants we can buy. Set up an equation where x = vegetable plants[/U]
2.75x = 24.75
Divide each side by 2.75
[B]x = 9[/B]

You have read a 247 page book for a class and decide to read 18 pages a night. How many pages are le

You have read a 247 page book for a class and decide to read 18 pages a night. How many pages are left in the book if you have been reading for n nights?
Set up the remaining pages read function R(n). We have:
[B]R(n) = 247 - 18n[/B]

You have to pay 29 a month until you reach 850 how many months will that take

You have to pay 29 a month until you reach 850 how many months will that take.
Let m be the number of months. We set up the inequality:
29m > = 850 <-- We want to know when we meet or exceed 850, so we use greater than or equal to
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=29m%3E%3D850&pl=Show+Interval+Notation']Type this inequality into our search engine[/URL], and we get:
m >= 29.31
We round up to the next integer month, to get [B]m = 30[/B].

You need to hire a catering company to serve meals to guests at a wedding reception. Company A charg

You need to hire a catering company to serve meals to guests at a wedding reception. Company A charges $500 plus $20 per guest. Company B charges $800 plus $16 per guest. For how many guests are the total costs the same at both companies?
Set up the Cost equations for both companies where g is the number of guests:
[LIST]
[*]C(a) = 20g + 500
[*]C(b) = 16g + 800
[/LIST]
Set each equation equal to each other and use our [URL='http://www.mathcelebrity.com/1unk.php?num=20g%2B500%3D16g%2B800&pl=Solve']equation solver[/URL] to get:
[B]g = 75[/B]

You open a hat stand in the mall with an initial start-up cost of $1500 plus 50 cents for every hat

You open a hat stand in the mall with an initial start-up cost of $1500 plus 50 cents for every hat you stock your booth with. a) What is your cost function?
Set up the cost function C(h) where h is the number of hats you stock:
C(h) = Cost per hat * h hats + Start Up Cost
[B]C(h) = 0.5h + 1500[/B]

You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a

You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a monthly fee of 160.00. Write and equation that represents your total cost Y in dollars after X months.
Set up the cost function Y where x is the number of months you rent
[B]Y = 160x + 510[/B]

You purchase a car for $23,000. The car depreciates at a rate of 15% per year. Determine the value

You purchase a car for $23,000. The car depreciates at a rate of 15% per year. Determine the value of the car after 7 years. Round your answer to the nearest cent.
Set up the Depreciation equation:
D(t) = 23,000/(1.15)^t
We want D(7)
D(7) = 23,000/(1.15)^7
D(7) = 23,000/2.66002
D(7) = [B]8,646.55[/B]

You purchase a new car for $35,000. The value of the car depreciates at a rate of 8.5% per year. If

You purchase a new car for $35,000. The value of the car depreciates at a rate of 8.5% per year. If the rate of decrease continues, what is the value of your car in 5 years?
Set up the depreciation function D(t), where t is the time in years from purchase. We have:
D(t) = 35,000(1 - 0.085)^t
Simplified, a decrease of 8.5% means it retains 91.5% of it's value each year, so we have:
D(t) = 35,000(0.915)^t
The problem asks for D(5)
D(5) = 35,000(0.915)^5
D(5) = 35,000(0.64136531607)
D(5) = $[B]22,447.79[/B]

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour?

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour?
Set up a proportion of text messages to minutes. Remember, there are 60 minutes in an hour, so we have:
9/12 = t/60 where t is the number of text messages in 60 minutes (1 hour)
[URL='https://www.mathcelebrity.com/prop.php?num1=9&num2=t&den1=12&den2=60&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this into the search engine[/URL], we get [B]t = 45[/B].

You started this year with $491 saved and you continue to save an additional $11 per month. Write an

You started this year with $491 saved and you continue to save an additional $11 per month. Write an algebraic expression to represent the total amount of money saved after m months.
Set up a savings function for m months
[B]S(m) = 491 + 11m[/B]

You use 4 gallons of water on 30 plants in your garden. At that rate, how much water will it take to

You use 4 gallons of water on 30 plants in your garden. At that rate, how much water will it take to water 45 plants?
Set up a proportion of gallons to plants:
4/30 = x/45 where x is the gallons of water needed for 45 plants.
Use our [URL='http://www.mathcelebrity.com/prop.php?num1=4&num2=x&den1=30&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL]:
[B]x = 6[/B]

You were able to send 30 snapchat stories in 9 minutes. At this rate, how many snapchat stories can

You were able to send 30 snapchat stories in 9 minutes. At this rate, how many snapchat stories can you send in 21 minutes?
Set up a proportion of stories to minutes where s is the number of Snapchat stories you can send in 21 minutes:
30/9 = s/21
To solve this proportion for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=30&num2=s&den1=9&den2=21&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
s = [B]70[/B]

Your clothes washer stopped working during the spin cycle and you need to get a person in to fix the

Your clothes washer stopped working during the spin cycle and you need to get a person in to fix the washer. Company A costs $20 for the visit and $15 for every hour the person is there to fix the problem. Company B costs $40 for the visit and $5 for every hour the person is there to fix the problem. When would Company B be cheaper than Company A?
Set up the cost functions:
[LIST]
[*]Company A: C(h) = 15h + 20
[*]Company B: C(h) = 5h + 40
[/LIST]
Set them equal to each other:
15h + 20 = 5h + 40
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=15h%2B20%3D5h%2B40&pl=Solve']equation solver[/URL], we get h = 2.
With [B]h = 3[/B] and beyond, Company B becomes cheaper than Company A.

Your mother gave you $13.32 With which to buy a present. This covered 3/5 of the cost. How much did

Your mother gave you $13.32 With which to buy a present. This covered 3/5 of the cost. How much did the present cost
Let the present cost p. We set up the equation we're given:
3/5p = 13.32
[URL='https://www.mathcelebrity.com/1unk.php?num=3%2F5p%3D13.32&pl=Solve']Type this equation into our search engine[/URL] and we get:
p = [B]$22.20[/B]

Youre setting sales goals for next month. You base your goals on previous average sales. The actual

Youre setting sales goals for next month. You base your goals on previous average sales. The actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units. What is the average number of units you can expect to sell next month?
Find the average sales for the last four years:
Average Sales = Total Sales / 4
Average Sales = (24 + 30 + 23 + 27) / 4
Average Sales = 104 / 4
Average Sales = [B]26 units[/B]

Zach can read 7 pages of a book in 5 minutes. At this rate, how long will it take him to read the en

Zach can read 7 pages of a book in 5 minutes. At this rate, how long will it take him to read the entire 175 page book?
Set up a proportion of pages to minutes where m is the number of minutes needed to read 175 pages:
7/5 = 175/m
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=7&num2=175&den1=5&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine [/URL]and we get:
m = [B]125 minutes or 2 hours and 5 minutes[/B]

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same a

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same as subtracting 5 from the number then multiplying by 4.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We're given two expressions in relation to this number (x):
[U]She subtracts 6 then multiplies the result by 5[/U]
[LIST]
[*]Subtract 6: x - 6
[*]Multiply the result by 5: 5(x - 6)
[/LIST]
[U]She subtracts 5 from the number then multiplying by 4[/U]
[LIST]
[*]Subtract 6: x - 5
[*]Multiply the result by 5: 4(x - 5)
[/LIST]
Finally, the expression [I]is the same as[/I] means an equation, so we set the first expression equal to the second expression to make the following equation:
5(x - 6) = 4(x - 5)
Now, let's solve the equation for x. To do this, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%28x-6%29%3D4%28x-5%29&pl=Solve']type this equation into our search engine [/URL]and we get:
x = [B]10[/B]

Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it tak

Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it take for the population of about 600,000 to turn into zombies?
Let d = every 2 days. We set up the exponential equation
2 * 2^d = 600,000
Divide each side by 2:
2^d = 300000
To solve this equation for d, we [URL='https://www.mathcelebrity.com/natlog.php?num=2%5Ed%3D300000&pl=Calculate']type it in our math engine[/URL] and we get
d = 18.19 (2 day periods)
18.19 * days per period = 36.38 total days
Most problems like this ask you to round to full days, so we round up to [B]37 days[/B].

|(x-7)/5|<=4

|(x-7)/5|<=4
Set up two equations:
[LIST=1]
[*](x-7)/5 <= 4
[*](x-7)/5 > -4
[/LIST]
Cross Multiply (1):
x - 7 <= 20
Add 7 to each side:
x <= 27
Cross Multiply (2):
x - 7 > -20
Add 7 to each side:
x > -13