number set - a collection of numbers
$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 DigitsFree π Digits Calculator - Calculates PI (π) to a set number of decimal places using the Gauss-Legendre Algorithm.
-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]
1/2, 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 -201/3 of the sum of a number and 2 plus 5 is -20
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
the sum of a number and 2:
x + 2
1/3 of the sum of a number and 2
1/3(x + 2)
1/3 of the sum of a number and 2 plus 5
1/3(x + 2) + 5
The phrase [I]is[/I] means equal to, so we set 1/3(x + 2) + 5 equal to -20:
[B]1/3(x + 2) + 5 = -20[/B]
1/4 of the difference of 6 and a number is 2001/4 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 times a number is 42010 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
12 is multiplied by some number, that product is reduced by 9, and the total is equal to 3712 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 number12 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 72A 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 minutes to answer 4 problems. how many minutes would it take to answer 22 questions13 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]
15 added to a number is 16 times the number15 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]
2 cards have different expressions written on them.: 5y - 2 and 3y + 10. for what value of y do the2 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 times a number equals that number plus 52 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 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 42 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]
2/3 of a number 17 is at least 292/3 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]
3 people can build a shed in 8 hours, how long would it take 5 people3 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 number3 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, 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]
4 machines can complete a job in 6 hours how long will it take 3 machines to complete the same jobs?4 machines can complete a job in 6 hours how long will it take 3 machines to complete the same jobs?
Set up a proportion of machines to hours where h is the number of hours that 3 machines take:
4/6 = 3/h
[URL='https://www.mathcelebrity.com/prop.php?num1=4&num2=3&den1=6&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get:
h = [B]4.5[/B]
4 teaspons of vegetable oil and 6 teaspoons of vinegar. 20 teaspoons of vegetable oil to how many te4 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 364 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 784 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
4subtractedfrom6timesanumberis324 subtracted from 6 times a number is 32.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
6 times this number means we multiply by x by 6
6x
4 subtracted from this expression means we subtract 4
6x - 4
The phrase [I]is[/I] means an equation, so we set 6x - 4 equal to 32
[B]6x - 4 = 32
[/B]
If you need to solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=6x-4%3D32&pl=Solve']type it in the search engine here[/URL].
5 is one-fourth of a number c5 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 subtracted from 3 times a number is 445 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 number5 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 35 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]
6 is one third of a number s6 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 66 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 686 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 number6 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 166 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 <-- This is our algebraic expression
Solve for x[/B]
Multiply through:
6x + 30 = 16
Subtract 30 from each side:
6x - 30 + 30 = 16 - 30
6x = -14
Divide each side by 6
6x/6 = -14/6
Simplify this fraction by dividing top and bottom by 2:
x = [B]-7/3
[MEDIA=youtube]oEx5dsYK7DY[/MEDIA][/B]
60 percent of a number minus 17 is -6560 percent of a number minus 17 is -65
Using our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=60&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percent to decimal calculator[/URL], we see that 60% is 0.6, so we have:
0.6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So 60% of a number is:
0.6x
Minus 17:
0.6x - 17
The word [I]is[/I] means an equation, so we set 0.6x - 17 equal to -65 to get our algebraic expression of:
[B]0.6x - 17 = -65[/B]
[B][/B]
If you want to solve for x in this equation, you [URL='https://www.mathcelebrity.com/1unk.php?num=0.6x-17%3D-65&pl=Solve']type it in our search engine and you get[/URL]:
[B]x = -80[/B]
7 is 1/4 of some number7 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 417 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 b7 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 times a number and 2 is equal to 4 times a number decreased by 87 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 number7 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
8 bags weigh 14 pounds. how much do 20 bags weigh8 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 more than twice a number is less than 6 more than the number8 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 is8 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 is one-third of a number x9 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 number9 is the sum of 7 and twice a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Twice a number means we multiply x by 2:
2x
The sum of 7 and twice a number
7 + 2x
The word [I]is[/I] mean equal to, so we set 7 + 2x equal to 9:
[B]7 + 2x = 9[/B]
9 less than 5 times a number is 3 more than 2x9 less than 5 times a number is 3 more than 2x
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
5 times a number means we multiply x by 5:
5x
9 less than 5x means we subtract 9 from 5x:
5x - 9
3 more than 2x means we add 3 to 2x:
2x + 3
The word [I]is[/I] means an equation, so we set 5x - 9 equal to 2x + 3:
[B]5x - 9 = 2x + 3 <-- This is our algebraic expression[/B]
[B][/B]
If you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-9%3D2x%2B3&pl=Solve']type this equation into the search engine[/URL], and we get:
x = [B]4[/B]
9 subtracted from the product of 3 and a number is greater than or equal to 169 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 109 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 39 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]
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}. FindA 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 tA 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 peopleA 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 booA 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 bakery has a fixed cost of $119.75 per a day plus $2.25 for each pastry. The bakery would like toA 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 bank charges a service fee of $7.50 per month for a checking account. A bank account has $85.00. IA 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 funcA 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 saA 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 bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The aveA 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 aA 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 avea 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 tA 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 booksA 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 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 rideA 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 iA 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 drinA 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 drinA 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 tA 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 - 0.3)^t
D(t) = 24000 * (0.7)^t
The problem asks for D(t)<=7300
24000 * (0.7)^t = 7300
Divide each side by 24000
(0.7)^t = 7300/24000
(0.7)^t= 0.30416666666
Take the natural log of both sides:
LN(0.7^t) = -1.190179482215518
Using the natural log identities, we have:
t * LN(0.7) = -1.190179482215518
t * -0.35667494393873245= -1.190179482215518
Divide each side by -0.35667494393873245
t = 3.33687437943
[B]Rounding this up, we have t = 4[/B]
A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the reA 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 rents $35 per day plus 15 cents per mile drivenA 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 ofa 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 manyA 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 provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 peA 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 checking account is set up with an initial balance of $2400 and $200 are removed from the accountA 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 260,000 people. Suppose that each year the population grows by 8.75% . WA 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 collection of 7 pencils, every week 3 more pencils are added How many weeks will it take to have 3a 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 numberA 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 thaA 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 uA 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 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 copy machine makes 28 copies per minute. how many copies does it make in 3 minutes and 45 secondsA 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 secondsA 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 fixeA 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 totA 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 eitheA 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 dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog waA 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. FA 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. FA 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 7A 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 giant tortoise can live 175 years in captivity. The gastrotrich, which is a small aquatic animal,A giant tortoise can live 175 years in captivity. The gastrotrich, which is a small aquatic animal, has a life-span of only 3 days (72 hours). If a gastrotrich died after 36 hours, a giant tortoise that lived 87.5 yeas would live proportionally the same because they both would have died halfway through their life-span.
How long would a giant tortoise live if it lived proportionally the same as a gastrotrich that died after 50 hours?
Set up a proportion of hours lived to lifespan where n is the number of years the giant tortoise lives:
50/72 = n/175
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=50&num2=n&den1=72&den2=175&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
n = [B]121.5[/B]
A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A starA 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 house painting company charges $376 plus $12 per hour. Another painting company charges $280 plusA 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 plusA 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 odd integers between 4 and 12A 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 local bank charges 19 per month plus 3 cents per check. The credit union charges7 per month plusA 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 iA 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 machine prints 230 movie posters each hour. Write and solve an equation to find the number of hourA 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 representsA 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 mechanic charges $45 per hour and parts cost $125. Write an expression for the total if the mechanA 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. HowA 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 monster energy drink has 164 mg of caffeine. Each hour your system reduces the amount of caffeineA 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 anA 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 eqA 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 equaA 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 vA 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 cA 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 numbera 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 12A 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 10A 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 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 andA 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 nA 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 tgA 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 photographer snapped 224 photos over a period of 15 days. At this rate, how many would he take inA 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 quarteA pile of coins, consisting of quarters and half dollars, is worth 11.75. If there are 2 more quarters than half dollars, how many of each are there?
Let h be the number of half-dollars and q be the number of quarters. Set up two equations:
(1) q = h + 2
(2) 0.25q + 0.5h = 11.75
[U]Substitute (1) into (2)[/U]
0.25(h + 2) + 0.5h = 11.75
0.25h + 0.5 + 0.5h = 11.75
[U]Group h terms[/U]
0.75h + 0.5 = 11.75
[U]Subtract 0.5 from each side[/U]
0.75h = 11.25
[U]Divide each side by h[/U]
[B]h = 15[/B]
[U]Substitute h = 15 into (1)[/U]
q = 15 + 2
[B]q = 17[/B]
A plant is 15 cm high and grows 4.5 cm every month. How many months will it take until the plant isA 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 hA 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 pot of soup, currently 66°C above room temperature, is left out to cool. If that temperature diffeA 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 prints 2 photos each minute. Let P be the number of photos printed in M minutes. Write anA 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 STAT200 weekly study times in hours is as follows: 2 15 15 18 30 Find the samA 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 that makes 25 oatmeal cookies calls for 2.5 cups of oats and one cup of sugar. Jerry needsA 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 neeA recipe calls for 2 tablespoons of olive oil for every 3 servings. How much olive oil will be needed for 6 servings?
Set up a proportion of tablespoons to servings:
2/3 = o/6 where o is the number of tablespoons per 6 servings.
[URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=o&den1=3&den2=6&propsign=%3D&pl=Calculate+missing+proportion+value']Type 2/3 = o/6 into our search engine[/URL], and we get [B]o = 4[/B].
A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation tA 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 anA 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 sA 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 salesperson drove 9 hours. How long will he have driven t hours later?Set up a function where t is the number of hours driven, and f(t) is the distance driven after t hours:
[B]f(t) = 9t[/B]
A school spent $150 on advertising for a breakfast fundraiser. Each plate of food was sold for $8.00A 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. ThA 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 rideA service charges a $1.95 flat rate plus $0.05 per mile. Jason only has $12 to spend on a a ride.
Set up the cost equation C(m) where m is the number of miles:
C(m) = 0.05m + 1.95
The problems asks for the number of miles (m) when C(m) = 12:
0.05m + 1.95 = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05m%2B1.95%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = [B]201[/B]
A set of 19 scores has a mean of 6.3. A new score of 8 is then included in the data set. What is thA 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 shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of packageA 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 soccer team is buying T-shirts to sell as a fundraiser. The team pays a flat fee of $35 for a logoA 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 droppingA 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 spinnA 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 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 student has $50 in saving and earns $40 per week. How long would it take them to save $450a 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 andA suitcase contains nickels, dimes and quarters. There are 2&1/2 times as many dimes as nickels and 5 times the number of quarters as the number of nickels. If the coins have a value of $24.80, how many nickels are there in the suitcase?
Setup number of coins:
[LIST]
[*]Number of nickels = n
[*]Number of dimes = 2.5n
[*]Number of quarters = 5n
[/LIST]
Setup value of coins:
[LIST]
[*]Value of nickels = 0.05n
[*]Value of dimes = 2.5 * 0.1n = 0.25n
[*]Value of quarters = 5 * 0.25n = 1.25n
[/LIST]
Add them up:
0.05n + 0.25n + 1.25n = 24.80
Solve for [I]n[/I] in the equation 0.05n + 0.25n + 1.25n = 24.80
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(0.05 + 0.25 + 1.25)n = 1.55n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
1.55n = + 24.8
[SIZE=5][B]Step 3: Divide each side of the equation by 1.55[/B][/SIZE]
1.55n/1.55 = 24.80/1.55
n = [B]16[/B]
[B]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05n%2B0.25n%2B1.25n%3D24.80&pl=Solve']Source[/URL][/B]
A super deadly strain of bacteria is causing the zombie population to double every day. Currently, tA 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 peopA 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 thA 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 sA 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 sA 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 toA 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 $0.65 per mile. If Erica has at most 10$ toA 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 $0.65 per mile. If Erica has at most 10$ toA 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 speA 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.
[MEDIA=youtube]mFqUe2mjX-w[/MEDIA]
A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 poinA 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 messageA 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 tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance wasA 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 populatA 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. TA 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 tree grows 35 cm in 2 years. If it continues to grow at the same rate determine how long it wouldA 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 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 hA 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]
Al's Rentals charges $25 per hour to rent a sailboard and a wetsuit. Wendy's Rentals charges $20 perAl'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]
Alorah joins a fitness center. She pays for a year plus a joining fee of $35. If the cost for the enAlorah 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 eaAmara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
Let the number of tv's be t. Set up the salary function S(t):
S(t) = Commision * tv's sold + Salary
Company A:
S(t) = 100t + 17,000
Company B:
S(t) = 20t + 29,000
The problem asks for how many tv's it takes to make both company salaries equal. So we set the S(t) functions equal to each other:
100t + 17000 = 20t + 29000
[URL='https://www.mathcelebrity.com/1unk.php?num=100t%2B17000%3D20t%2B29000&pl=Solve']Type this equation into our search engine[/URL] and we get:
t = [B]150[/B]
Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and inAmy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and inside. Amy charges 40$ 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 auto repair bill is $126 for parts and $35 for each hour of labor. If h is the number of hours ofAn 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 interior designer charges $100 to visit a site, plus $55 to design each room. Identify a functionAn 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]
Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. WhatAngad 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 colAngelica’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 tAnn 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 lonAnna 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 lAs 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 dogsAt 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 youAt 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. NonmeAt 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. NonmembeAt 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]
Austin needs $240 to buy a new bike if he can save $16 per week and how many weeks can you purchaseAustin 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].
Balls numbered 1 to 10 are placed in a bag. Two of the balls are drawn out at random. Find the probaBalls 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 willBarney 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 StatisticsFree Basic Statistics Calculator - Given a number set, and an optional probability set, this calculates the following statistical items:
Expected Value
Mean = μ
Variance = σ2
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]
Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half ofBenny 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 admissioBeverly 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 $0.20 per mileBills car rental charges a base fee of 50$ 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]
Bridget can grow 6 flowers with every seed packet. With 4 seed packets, how many total flowers can BBridget 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
Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly havCarly 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 untiCarly 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]
Cassidy is renting a bicycle on the boardwalk. The rental costs a flat fee of $10 plus an additionalCassidy 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. AnotherCathy 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]
Clara can bake 17 cookies with each scoop of flour. With two scoops of flour, how many cookies can CClara 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.
Colin was thinking of a number. Colin divides by 8, then adds 1 to get an answer of 2. What was theColin 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]
Company a charges $25 plus $0.10 a mile. Company b charges $20 plus $0.15 per mile. How far would yoCompany 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 $0.0Company 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 fCongratulations!! 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]
Construct a data set of seven temperature readings where the mean is positive and the median is negaConstruct 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]
Craig went bowling with $25 to spend. He rented shoes for $5.25 and paid $4.00 for each game. What wCraig 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].
D= {a,b,c,d,e,f,g} the cardinality of set D isD= {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's school is planning a field trip to an art museum. Bus company A charges a $60 rental fee plusDan'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]
DeAndre is a spelunker (someone who explores caves). One day DeAndre is exploring a cave that has aDeAndre 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 DebbieDebbie 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 possibleDebra 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]
Dedra took a total of 6 pages of notes during 2 hours of class. After attending 3 hours of class, hoDedra took a total of 6 pages of notes during 2 hours of class. After attending 3 hours of class, how many total pages of notes will Dedra have in her notebook?
Set up a proportion of pages of notes to hours of class where p equals the number of pages of notes Dedra takes for 3 hours of class:
6/2 = p/3
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=p&den1=2&den2=3&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
p = [B]9[/B]
Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened upDeon 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]
Deyjiana reads 30 pages in 25 minutes. If she reads 210 pages at this rate, how long will it take heDeyjiana 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 nuDiana earns $8.50 working as a lifeguard. Write an equation to find Dianas money earned m for any numbers of hours h
Set up the revenue function:
[B]R = 8.5h[/B]
difference between 2 positive numbers is 3 and the sum of their squares is 117difference 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
Dr. Carlson is contemplating the impact of an antibiotic on a particular patient. The patient will tDr. 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 tDr. 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 offersDunder 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 spendDylans 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 reporEach 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]
Elsa took a total of 25 quizzes over the course of 5 weeks. After attending 8 weeks of school this qElsa 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]
Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, whEthan 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 NumbersFree Even Numbers Calculator - 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 ofEvery 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]
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 themFarmer 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 ValueUsing 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]
Fixed cost 500 marginal cost 8 item sells for 30fixed 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 2Four 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]
Fundamental Rule of CountingFree Fundamental Rule of Counting Calculator - Given a set of items, this calculates the total number of groups/choices that can be formed using the rule of product.
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]
Giovanni is thinking of a number. If he adds 2 to it, then divides that sum by 3, he gets 7. What isGiovanni 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]
Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking aGraham 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 MeanFree Grand Mean Calculator - 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 GraysonGrayson 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]
Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (ThinkGym 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]
Hall looked at 10 websites every 35 hours. At this rate, how long, in hours, will it take to look atHall looked at 10 websites every 35 hours. At this rate, how long, in hours, will it take to look at 6 websites?
Set up a proportion of websites to hours where h is the number of hours it takes to look at 6 websites:
10/35 = 6/h
To solve this proportion for h, we [URL='https://www.mathcelebrity.com/prop.php?num1=10&num2=6&den1=35&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
h = [B]21 hours[/B]
Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $1Happy 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 $1Happy 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 ofHari 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.
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
How long does it take to cook 20 eggs if it takes 10 minutes to cook 4 eggsHow long does it take to cook 20 eggs if it takes 10 minutes to cook 4 eggs
Set up a proportion of minutes to eggs where m is the number of minutes it takes for 20 eggs.
10 minutes / 4 eggs = m/20
[URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=10&num2=m&den1=4&den2=20&propsign=%3D&pl=Calculate+missing+proportion+value']Solving for m[/URL], we get:
m = 50
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]
I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5I 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 4I 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 sI 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 aI 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 13I 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 make 750 toys in 10 hours how many can I make in 4 minutesI 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 starteI 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 donutsIf 1/2 cup of milk makes 8 donuts. How much cups it takes to make 28 donuts?
Set up a proportion of cups to donuts, where c is the number of cups required to make 28 donuts:
1/2/8 = c/28
Cross multiply:
28(1/2) = 8c
8c = 14
[URL='https://www.mathcelebrity.com/1unk.php?num=8c%3D14&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]c = 1.75[/B]
If 11 times a number is added to twice the number, the result is 104If 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 thIf 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 gallonsIf 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 hoursIf 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 3.75 inches on a map are equal to 18.75 miles, how many miles are 5 inches equal to?If 3.75 inches on a map are equal to 18.75 miles, how many miles are 5 inches equal to?
Set up a proportion of inches to miles where m is the number of miles for 5 inches:
3.75/18.75 = 5/m
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3.75&num2=5&den1=18.75&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
m = [B]25 miles[/B]
If 4 times a number is added to 9, the result is 49If 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 peopleIf 50 out of 250 people die. How many people died per 10 people
We set up a proportion of deaths to total people where d is the number of deaths for 10 people. We have:
50/250 = d/10
To solve this proportion for d, we [URL='https://www.mathcelebrity.com/prop.php?num1=50&num2=d&den1=250&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
d = [B]2[/B]
If 72 is added to a number it will be 4 times as large as it was originallyIf 72 is added to a number it will be 4 times as large as it was originally
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
72 added to a number:
x + 72
4 times as large as it was originally means we take the original number x and multiply it by 4:
4x
Now, the phrase [I]it will be[/I] means an equation, so we set x + 72 equal to 4x to get our final algebraic expression:
[B]x + 72 = 4x[/B]
[B][/B]
If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B72%3D4x&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]24[/B]
If 9 is added to 1/3 of a number, the result is 15. What is the number?If 9 is added to 1/3 of a number, the result is 15. What is the number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
1/3 of a number means we multiply x by 1/3:
x/3
9 is added to 1/3 of a number:
x/3 + 9
The phrase [I]the result is[/I] means an equation. so we set x/3 + 9 equal to 15
x/3 + 9 = 15
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2F3%2B9%3D15&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]18[/B]
if 9 times a number is decreased by 6, the result is 111if 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 20if 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 26If 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 60if 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 an employee starts saving with $750 and increases his savings by 8% each month, what will be hisIf 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 Bill's salary is $25 and he gets a 20¢ commission on every newspaper he sells, how many must he sIf 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 minutesIf 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 from twice a number you subtract four, the difference is twentyThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Twice a number means we multiply x by 2:
2x
Subtract four:
2x - 4
The word [I]is [/I]means equal to. We set 2x - 4 equal to 20 for our algebraic expression:
[B]2x - 4 = 20
[/B]
If the problem asks you to solve for x:
we [URL='https://www.mathcelebrity.com/1unk.php?num=2x-4%3D20&pl=Solve']plug this equation into our calculator [/URL]and get x = [B]12[/B]
If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it takeIf 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 numberIf 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 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 the difference of a number and 4 is multiplied by 3 the result is 19If 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 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 numberIf 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 -28If 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 you add 35 to twice a number, the result is 17. What is the number?if you add 35 to twice a number, the result is 17. What is the number?
A number is represented by a variable, let's call it "x".
Twice a number means we multiply by 2 --> 2x
Add 35
2x + 35
Now set that entire expression equal to 17
2x + 35 = 17
[URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B35%3D17&pl=Solve']Plug that into the search engine to solve for x[/URL]
[B]x = -9[/B]
If you can buy 1?3 of a box of chocolates for 6 dollars, how much can you purchase for 4 dollars? WrIf you can buy 1?3 of a box of chocolates for 6 dollars, how much can you purchase for 4 dollars? Write your answer as a fraction of a box.
Set up a proportion of dollars to boxes where b is the number of boxes for $4:
6/1/3 = 4/b
Cross multiply:
6b = 4/3
Multiply each side by 1/6 to isolate b:
b = 4/18
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=4&num2=18&num3=&pl=GCF+and+LCM']Type in GCF(4,18) into the search engine[/URL]. We get a greatest common factor of 2.
Divide 4 and 18 in the fraction by 2. We get the reduced fraction of:
[B]b = 2/9[/B]
If you have $272, and you spend $17 each day, how long would it be until you had no money left?If you have $272, and you spend $17 each day, how long would it be until you had no money left?
Let d be the number of days. We have a balance expression of:
272 - 17d
We want to know when the balance is 0, so we set 272 - 17d equal to 0.
272 - 17d = 0
To solve for d, we [URL='http://272 - 17d = 0']type this equation into our search engine[/URL] and we get:
d = [B]16[/B]
Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He rImagine 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 rImagine 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 rImagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. The researcher posed a null hypothesis that the average weight for boys in that high school should be 100 lbs. What is the [B][U]absolute value[/U][/B] of calculated t that we use for testing the null hypothesis?
Mean is 109.4 and Standard Deviation = 20.79182532 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']statistics calculator[/URL]
Now use those values and calculate the t-value
Abs(t value) = (100 - 109.4)/ 20.79182532/sqrt(5)
Abs(tvalue) = [B]1.010928029[/B]
In 2010 a algebra book cost $125. In 2015 the book cost $205. Whats the linear function since 2010?In 2010 a algebra book cost $125. In 2015 the book cost $205. Whats the linear function since 2010?
In 5 years, the book appreciated 205 - 125 = 80 in value.
80/5 = 16.
So each year, the book increases 16 in value. Set up the cost function:
[B]C(y) = 16y where y is the number of years since 2010[/B]
In a basketball game, you make 8 of 20 free throws. If you continue this for the next 50 free throwsIn 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 & tIn 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]
Isabel is making face mask. She spends $50 on supplies and plans on selling them for $4 per mask. HoIsabel 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 nuIsabel 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 forit 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 repreIt 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 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 takeIt 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]
Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how manyJenny 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. HoJenny 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 inJessica 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]
Jim has $440 in his savings account and adds $12 per week to the account. At the same time, Rhonda hJim 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 waJim 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 buJody 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 opens a bank account that starts with $20 and deposits $10 each week. Bria has a different accouJoe 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 forJohn is paid a retainer of $550 a week as well as a 2% commission on sales made. Find his income for the week if in one week he sells cars worth of $80000
Set up the income function C(s) where s is the number of sales for a week. Since 2% can be written as 0.02, we have:
I(s) = Retainer + 2% of sales
I(s) = 550 + 0.02s
The problem asks for a I(s) where s = 80,000:
I(s) = 550 + 0.02(80000)
I(s) = 550 + 1600
I(s) = [B]2150[/B]
John read the first 114 pages of a novel, which was 3 pages less than 1/3John 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]
Julio had a coin box that consisted of only quarters and dimes. The number of quarters was three timJulio 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]
Karen earns $20 per hour and already has $400 saved, and wants to save $1200. How many hours until bKaren 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 perKarmen 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 $450
8h - 15 = 450
[URL='https://www.mathcelebrity.com/1unk.php?num=8h-15%3D450&pl=Solve']Typing 8h - 15 = 450 into the search engine[/URL], we get h = 58.13. We round this up to 59 hours.
keisha is babysitting at 8$ per hour to earn money for a car. So far she has saved $1300. The car thkeisha is babysitting at 8$ 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 aKeith 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].
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. WritKim 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 sheKimberly 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 anKrutika 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].
Leonard earned $100 from a bonus plus $15 per day (d) at his job this week. Which of the following eLeonard 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. ForLet 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]
Liam, a 19th century cowboy, carries an 1847 Colt single action 6 shooter revolver. So proficient isLiam, 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 GOMILily 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 thisLindsey 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 12M 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]
Mackenzie baked 12 cookies with 2 scoops of flour. How many scoops of flour does Mackenzie need in oMackenzie 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. MagMaggie 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 cMarcela 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 $500[/I]
[*]c < 120 [I]She also knows that she will make less than 120 chicken wings[/I]
[*]h < 100 [I]and less that 100 hot dogs[/I]
[/LIST]
Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are nowMaria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start?
Let the number of boxes Maria started with be b. We're given the following pieces:
[LIST]
[*]She starts with b
[*]She bought 7 boxes. So we add 7 to b: b + 7
[*]If half the boxes were destroyed, she's left with 1/2. So we divide (b + 7)/2
[*]Only 22 boxes left means we set (b + 7)/2 equal to 22
[/LIST]
(b + 7)/2 = 22
Cross multiply:
b + 7 = 22 * 2
b + 7 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B7%3D44&pl=Solve']Type this equation into our search engine[/URL] to solve for b and we get:
b = [B]37[/B]
Maria is saving money to buy a bike that cost 133$. She has 42$ and will save an additional 7 each wMaria 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]
Marla wants to rent a bike Green Lake Park has an entrance fee of $8 and charges $2 per hour for bikMarla 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 $14.50Mary 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]
Matt has $100 dollars in a checking account and deposits $20 per month. Ben has $80 in a checking acMatt 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]
Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how manyMegan 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 cMelissa 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]
Miguel has $80 in his bank and saves $2 a week. Jesse has $30 in his bank but saves $7 a week. In hoMiguel 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]
Mr. Chris’s new app “Tick-Tock” is the hottest thing to hit the app store since...ever. It costs $5Mr. 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 getsMr. 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 ofMr. 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 witMrs. 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
Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and suMultiply 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 9Multiplying 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.
Nancy shot a 16 on 4 holes of golf. At this rate, what can she expect her score to be if she plays 1Nancy 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 iNancy 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 thenandita earned $224 last month. she earned $28 by selling cards at a craft fair and the rest of the money by babysitting. Complete an equation that models the situation and can be used to determine x, the number of dollars nandita earned last month by babysitting.
We know that:
Babysitting + Card Sales = Total earnings
Set up the equation where x is the dollars earned from babysitting:
[B]x + 28 = 224[/B]
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B28%3D224&pl=Solve']type it in our math engine[/URL] and we get:
x = [B]196[/B]
Natural NumbersFree Natural Numbers Calculator - Shows a set amount of natural numbers and cumulative sum
Need Help on this problemWhat do you want to do with this number set? Express it as representation of integers?
Ning prepared 16 kilograms of dough after working 4 hours. How many hours did Ning work if he preparNing 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].
Notebooks cost $1.39 each. What are the possible numbers of notebooks that can be purchased with $10Notebooks 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 275Number 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 toOceanside 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 5Oceanside 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 NumbersFree Odd Numbers Calculator - 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 randomlyOf 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]
On a particular road map, 1/2 inch represents 18 miles. About how many miles apart are 2 towns thatOn 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]
One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels.One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels.
Set up our equation where b is the number of total bagels
72 = b/3
Multiply each side by 3
[B]b = 216[/B]
One-half a number is fiftyThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
One-half a number means we divide x by2:
x/2
The word [I]is[/I] means equal to. We set x/2 equal to 50 for our algebraic expression
[B]x/2 = 50
[/B]
If the problem asks us to solve for x, we cross multiply:
x = 2 * 50
x = [B]100[/B]
Orange Theory is currently offering a deal where you can buy a fitness pass for $100 and then each cOrange 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 suppliesOscar 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 neOur 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].
Paul can walk 15 steps in 5 minutes How long does it take Paul to walk 75 steps at the same speedPaul 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]
Permutations and CombinationsFree Permutations and Combinations Calculator - Calculates the following:
Number of permutation(s) of n items arranged in r ways = nPr
Number of combination(s) of n items arranged in r unique ways = nCr including subsets of sets
Peter was thinking of a number. Peter doubles it and adds 0.8 to get an answer of 31. Form an equatiPeter 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
please answer this word problemTime 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]
porportion problemsSet 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]
Prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and twImagine 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]
Prove there is no integer that is both even and oddLet us take an integer x which is both even [I]and[/I] odd.
[LIST]
[*]As an even integer, we write x in the form 2m for some integer m
[*]As an odd integer, we write x in the form 2n + 1 for some integer n
[/LIST]
Since both the even and odd integers are the same number, we set them equal to each other
2m = 2n + 1
Subtract 2n from each side:
2m - 2n = 1
Factor out a 2 on the left side:
2(m - n) = 1
By definition of divisibility, this means that 2 divides 1.
But we know that the only two numbers which divide 1 are 1 and -1.
Therefore, our original assumption that x was both even and odd must be false.
[MEDIA=youtube]SMM9ubEVcLE[/MEDIA]
Rachel saved $200 and spends $25 each week. Roy just started saving $15 per week. At what week willRachel 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 GeneratorFree Random Number Generator Calculator - This program generates (n) random numbers between a set of values you specify.
Example: Generate 5 random numbers between 0 and 100.
Renee sells 6 gifts in 20 minutes. How many might she sell in 4 hrsRenee 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 theRick 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 pageRicky 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]
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 NotationFree Roster Notation Calculator - Given a set of numbers, this displays the roster notation
Sally and Adam works a different job. Sally makes $5 per hour and Adam makes $4 per hour. They eachSally 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 caSalma 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 problemsSam 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 eaSam'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]
Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money froSarah 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. NextSarah 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 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}
[MEDIA=youtube]_O6nXX0V4zo[/MEDIA][/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.
[MEDIA=youtube]aQKLVxIB-p4[/MEDIA][/I]
Set D is the set of two-digit even numbers less than 67 that are divisible by 5Set 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 NotationFree Set Notation Calculator - 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 Jσ(A,B)
* 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 40Set of 2 digit even numbers less than 40
Knowns and givens:
[LIST]
[*]2 digit numbers start at 10
[*]Less than 40 means we do not include 40
[*]Even numbers are divisible by 2
[/LIST]
[B]{10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38}[/B]
Seth is constantly forgetting the combination to his lock. He has a lock with four dials. (Each ha 1Seth is constantly forgetting the combination to his lock. He has a lock with four dials. (Each has 10 numbers 0-9). If Seth can try one lock combination per second, how many seconds will it take him to try every possible lock combination?
Start with 0001, 0002, all the way to 9999
[URL='https://www.mathcelebrity.com/inclusnumwp.php?num1=0&num2=9999&pl=Count']When you do this[/URL], you get 10,000 combinations. One per second = 10,000 seconds
Seven less than 1/4 of a number is 9.Seven less than 1/4 of a number is 9.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
1/4 of a number means we multiply x by 1/4:
x/4
Seven less than this means we subtract 7 from x/4:
x/4 - 7
The word [I]is[/I] means an equation, so we set x/4 - 7 equal to 9:
[B]x/4 - 7 = 9[/B]
Sheila loaded 21 trucks every 28 minutes. At this rate how long will it take to load 12 trucksSheila 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 TestFree Sign Test Calculator - 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.
Six less than twice a number is at least -1 and at most 1First, 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
Sixteen subtracted from five times a number equals the number plus fourThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
5 times a number
5x
Sixteen subtracted from five times a number
5x - 16
the number plus 4:
x + 4
Equals means we set 5x - 16 equals to x + 4 for our algebraic expression:
[B]5x - 16 = x + 4[/B]
[B][/B]
If you have to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-16%3Dx%2B4&pl=Solve']type this expression into our math solver[/URL] and we get:
x = [B]5[/B]
Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cSoda 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]
Squaring a number equals 5 times that numberSquaring 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]
Students stuff envelopes for extra money. Their initial cost to obtain the information for the job wStudents 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 17sum of 3 consecutive odd integers equals 1 hundred 17
The sum of 3 consecutive odd numbers equals 117. What are the 3 odd numbers?
1) Set up an equation where our [I]odd numbers[/I] are n, n + 2, n + 4
2) We increment by 2 for each number since we have [I]odd numbers[/I].
3) We set this sum of consecutive [I]odd numbers[/I] equal to 117
n + (n + 2) + (n + 4) = 117
[SIZE=5][B]Simplify this equation by grouping variables and constants together:[/B][/SIZE]
(n + n + n) + 2 + 4 = 117
3n + 6 = 117
[SIZE=5][B]Subtract 6 from each side to isolate 3n:[/B][/SIZE]
3n + 6 - 6 = 117 - 6
[SIZE=5][B]Cancel the 6 on the left side and we get:[/B][/SIZE]
3n + [S]6[/S] - [S]6[/S] = 117 - 6
3n = 111
[SIZE=5][B]Divide each side of the equation by 3 to isolate n:[/B][/SIZE]
3n/3 = 111/3
[SIZE=5][B]Cancel the 3 on the left side:[/B][/SIZE]
[S]3[/S]n/[S]3 [/S]= 111/3
n = 37
Call this n1, so we find our other 2 numbers
n2 = n1 + 2
n2 = 37 + 2
n2 = 39
n3 = n2 + 2
n3 = 39 + 2
n3 = 41
[SIZE=5][B]List out the 3 consecutive odd numbers[/B][/SIZE]
([B]37, 39, 41[/B])
37 ? 1st number, or the Smallest, Minimum, Least Value
39 ? 2nd number
41 ? 3rd or the Largest, Maximum, Highest Value
sum of a number and 7 is subtracted from 15 the result is 6.Sum of a number and 7 is subtracted from 15 the result is 6.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take this expression in pieces. Sum of a number and 7
x + 7
Subtracted from 15
15 - (x + 7)
The result is means an equation, so we set this expression above equal to 6
[B]15 - (x + 7) = 6 <-- This is our algebraic expression[/B]
If the problem asks you to solve for x, we Group like terms
15 - x - 7 = 6
8 - x = 6
[URL='https://www.mathcelebrity.com/1unk.php?num=8-x%3D6&pl=Solve']Type 8 - x = 6 into the search engine[/URL], and we get [B]x = 2[/B]
Sum of a number and it's reciprocal is 6. What is the number?Sum of a number and it's reciprocal is 6. What is the number?
Let the number be n.
The reciprocal is 1/n.
The word [I]is[/I] means an equation, so we set n + 1/n equal to 6
n + 1/n = 6
Multiply each side by n to remove the fraction:
n^2 + 1 = 6n
Subtract 6n from each side:
[B]n^2 - 6n + 1 = 0 [/B]<-- This is our algebraic expression
If the problem asks you to solve for n, then you [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-6n%2B1%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this quadratic equation into our search engine[/URL].
Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the populatSuppose 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 populatSuppose 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 doeSuppose 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 the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gaSuppose 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 poSuppose 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 $16Suppose 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].
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]
Ten subtracted from the product of 9 and a number is less than ?24Ten 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 teTerry 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. WhaThe 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 25.5Let 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 basketball team is selling candy as a fundraiser. A regular candy bar cost 0.75 and a king sizedThe 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 $46The 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 regarThe 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 schedThe 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 anThe 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 theThe cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the total cost to park for 5 hours?
Set up our equation where C is cost and h is the number of hours used to park
C = 1.5h + 2.25
With h = 5, we have:
C = 1.5(5) + 2.25
C = 7.5 + 2.25
C = 9.75
The cost of a field trip is $220 plus $7 per student. If the school can spend at most $500, how manyThe cost of a field trip is $220 plus $7 per student. If the school can spend at most $500, how many students can go on the field trip?
Set up the inequality where s is the number of students:
C(s) = 220 + 7s
We want C(s) <= 500, since at most means no more than
220 + 7s <= 500
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=220%2B7s%3C%3D500&pl=Solve']inequality calculator[/URL], we get:
[B]s <= 40[/B]
The cost of a taxi ride is $1.2 for the first mile and $0.85 for each additional mile or part thereoThe 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 kilomeThe cost of hiring a car for a day is $60 plus 0.25 cents per kilometer. Michelle travels 750 kilometers. What is her total cost
Set up the cost function C(k) where k is the number of kilometers traveled:
C(k) = 60 + 0.25k
The problem asks for C(750)
C(750) = 60 + 0.25(750)
C(750) = 60 + 187.5
C(750) = [B]247.5[/B]
The cost of tuition at Johnson Community College is $160 per credit hour. Each student also has to pThe 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 textbooks if one textbook costs $140The 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 oThe cost to rent a construction crane is 450 per day plus 150 per hour. What is the maximum number of hours the crane can be used each day if the rental cost is not to exceed 1650 per day?
Set up the cost function where h is the number of hours:
C(h) = 150h + 450
We want C(h) <= 1650:
150h + 450 <= 1650
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=150h%2B450%3C%3D1650&pl=Solve']equation/inequality solver[/URL], we get:
[B]h <= 8[/B]
The dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for eachThe 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 number and 9 is 27. Find that numberThe 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 169The difference between two positive numbers is 5 and the square of their sum is 169.
Let the two positive numbers be a and b. We have the following equations:
[LIST=1]
[*]a - b = 5
[*](a + b)^2 = 169
[*]Rearrange (1) by adding b to each side. We have a = b + 5
[/LIST]
Now substitute (3) into (2):
(b + 5 + b)^2 = 169
(2b + 5)^2 = 169
[URL='https://www.mathcelebrity.com/community/forums/calculator-requests.7/create-thread']Run (2b + 5)^2 through our search engine[/URL], and you get:
4b^2 + 20b + 25
Set this equal to 169 above:
4b^2 + 20b + 25 = 169
[URL='https://www.mathcelebrity.com/quadratic.php?num=4b%5E2%2B20b%2B25%3D169&pl=Solve+Quadratic+Equation&hintnum=+0']Run that quadratic equation in our search engine[/URL], and you get:
b = (-9, 4)
But the problem asks for [I]positive[/I] numbers. So [B]b = 4[/B] is one of our solutions.
Substitute b = 4 into equation (1) above, and we get:
a - [I]b[/I] = 5
[URL='https://www.mathcelebrity.com/1unk.php?num=a-4%3D5&pl=Solve']a - 4 = 5[/URL]
[B]a = 9
[/B]
Therefore, we have [B](a, b) = (9, 4)[/B]
The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the numThe 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 nThe 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 domain of a relation is all even negative integers greater than -9. The range y of the relationThe 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 currentlyThe 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 grass in jamie’s yard grew 16 centimeters in 10 days. how many days did it take for the grass tothe 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 larger of 2 numbers is 1 more than 3 times the smaller numberThe 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 mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. WhThe 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 principal randomly selected six students to take an aptitude test. Their scores were: 87.4 86.9First, 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 13the 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 and 15 is not less than 15the product of a number and 15 is not less than 15
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
the product of a number and 15 means we multiply x by 15
15x
The phrase [I]not less than[/I] means greater than or equal to. We set 15x greater than prequel to 15
[B]15x >= 15 <-- This is our algebraic expression
[/B]
[U]If the problem asks you to solve for x:[/U]
Divide each side by 15:
15x/15 >= 15/15
[B]x >= 1[/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 4 more than a number and 7 is 10the 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 ratio of men to women working for a company is 3 to 4. If there are 81 men working for the compaThe 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 votesThe 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 votesThe 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 scale on a map is 1 inch = 60 miles. If two cities are 75 miles apart, how far apart are they onThe 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 forThe 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 howThe 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 odd numbers between 10 and 30The 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 natural numbers less than 7 that are divisible by 3the 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 23The 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 sum of 6 and 7, plus 5 times a number, is -12the 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 a number and 16 is eA 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 17The 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 5/2the 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 72The 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 3The 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 17the 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 160the 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 17The 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 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 numberThe 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 three times a number and 18 is -39. Find the numberThe 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 total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25The total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25
[U]Set up the cost function:[/U]
Cost function = Fixed Cost + Variable Cost per Unit * Number of Units
[U]Plug in Fixed Cost = 2900 and Cost per Unit = $25[/U]
[B]C(x) = 2900 + 25x
[MEDIA=youtube]77PiD-VADjM[/MEDIA][/B]
The total cost to fix your bike is $45 the parts cost $10 and the labor cost seven dollars per hourThe 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 volleyball team and the wrestling team at Clarksville High School are having a joint car wash tThe 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]
There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. HowThere 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 40 grams in 5 prunes. How much gram of weight is in 34 prunesThere 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 oThere 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 64 members in the history club. 11 less than half of the members are girls. How many membeThere 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 is a ratio of 5 girls to 3 boys in the chorus. There are 24 boys in the chorus.How many girlsThere 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].
[MEDIA=youtube]c-xshqvfvig[/MEDIA]
Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quoThink 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 numberThirty 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 DistanceLet 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 DistanceThank 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]
To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional poTo 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 iToday 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 hisTom 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 departmTom 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]
Trimmed Mean and Winsorized MeanFree Trimmed Mean and Winsorized Mean Calculator - Given a number set and a trimmed mean percentage, this will calculate the trimmed mean (truncated mean) or winsorized mean.
True False EquationsFree True False Equations Calculator - 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 varianceTrue 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 Ac)=1, where Ac 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]
Twenty-five is nine more than four times a numberThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Four times a number:
4x
nine more than four times a numbrer
4x + 9
The phrase [I]is[/I] means equal to. We set 4x + 9 equal to 25 as our algebraic expression:
[B]4x + 9 = 25
[/B]
If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D25&pl=Solve']type it in our math solver[/URL] and get:
x = [B]4[/B]
Twenty-five is the same as ten added to twice a numberThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Twice a number means we multiply x by 2:
2x
ten added to twice a number
2x + 10
The phrase [I]is the same as [/I]means equal to. Set 25 equal to 2x + 10 to get our algebraic expression
[B]25 = 2x + 10
[/B]
If the problem asks you to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=25%3D2x%2B10&pl=Solve']type it in our math solver [/URL]and get
x = [B]7.5[/B]
Twice a number decreased by eight is zeroThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Twice a number:
2x
decreased by eight
2x - 8
[I]is [/I]means equal to. Set 2x - 8 equal to zero for our algebraic expression:
[B]2x - 8 = 0
[/B]
If the problem asks you to solve for x, add 8 to each side:
2x = 8
Divide each side by 2:
x= [B]4[/B]
twice the difference between x and 28 is 3 times a numbertwice 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 2twice 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 8twice 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 23twice 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 number and 6 is equal to three times the difference of the number and 3. Find the[SIZE=6]Twice the sum of a number and 6 is equal to three times the difference of the number and 3. Find the number.
The phrase [/SIZE][I][SIZE=7]a number[/SIZE][/I][SIZE=6] means an arbitrary variable, let's call it x.
The sum of a number and 6 means we add 6 to x:
x + 6
Twice the sum of a number and 6 means we multiply x + 6 by 2:
2(x + 6)
the difference of the number and 3 means we subtract 3 from x
x - 3
three times the difference of the number and 3 means we multiply x - 3 by 3:
3(x- 3)
The word [I]is[/I] means we set 2(x + 6) equal to 3(x - 3)
2(x + 6) = 3(x - 3)
Use the distributive property to multiply through:
2x + 12 = 3x - 9
Subtract 2x from each side:
2x - 2x + 12 = 3x - 2x - 9
x - 9 = 12
Add 9 to each side:
x - 9 + 9 = 12 + 9
x = [B]21[/B]
[B][/B]
[B][MEDIA=youtube]CeZl_oZnSiw[/MEDIA][/B][/SIZE]
two numbers have an average of 2100 and one number is $425 more than the other number. What are thetwo 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 numbersLet the numbers be x and y. Set up our givens:
[LIST=1]
[*]x + y = 83
[*]x - y = 17
[/LIST]
[U]Add equation (1) to equation (2)[/U]
x + x + y - y = 83 + 17
[U]The y-terms cancel out:[/U]
2x = 100
[U]Divide each side by 2:[/U]
2x/2= 100/2
x = [B]50[/B]
[U]
Plug x = 50 into equation (1)[/U]
50 + y = 83
[U]Subtract 50 from each side:[/U]
50 - 50 + y = 83 - 50
[U]Cancel the 50 on the left side:[/U]
y = [B]33
[/B]
So our two numbers (x, y) = (33, 50)
[MEDIA=youtube]jajO043ChUM[/MEDIA]
Video store movie rental plans. Plan A 25 membership fee plus 1.25 for movie. Plan B 40 for unlimiteVideo 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.
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
what is a well defined setwhat 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 SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512WHAT 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 43A 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 negatiWhen 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 unknWhen 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 numWhen 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 numWhen 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 31When 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 twice a number is reduced by 15 you get 95 what is the numberWhen 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 NumbersFree Whole Numbers Calculator - 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 theWrite 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}
x is a multiple of 6 and 1 ? x ? 16x 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]
y is the sum of twice a number and 3y 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]
You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $1You 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 nYou 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 sameYou 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 bakedYou 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 $5You 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 using a spinner with the numbers 1-10 on it. Find the probability that the pointer will stoYou 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 get 2 different moving companies to help you move. The first one charges $150 up front thenYou 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 $8You 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 aYou 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 to pay 29 a month until you reach 850 how many months will that takeYou 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 chargYou 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 hatYou 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 aYou 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 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 were able to send 30 snapchat stories in 9 minutes. At this rate, how many snapchat stories canYou 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]
Youre setting sales goals for next month. You base your goals on previous average sales. The actualYoure 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 enZach 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 aZalika 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]
