Question

1.) You are making 6 quarts of fruit punch for a party. You want the punch to contain 80% fruit juice. You have bottles of 100% fruit juice and 20% fruit juice. How many quarts of 100% fruit juice and how many quarts of 20% fruit juice should you mix to make 6 quarts of 80% fruit juice?
2.) A business center charges a flat fee to send faxes plus a fee per page you send one fax with 4 pages for $5.36 and another fax with 7 pages for $7.88.Find the flat fee and the cost per page to send a fax.

Answer 1

Question 1: Get 6 qt of 80% juice with 100% juice and 20% juice.
Change the percents to decimals (.8, 1, and .2)
To model 6 quarts of 80% juice, write as 6(.8)
To model an unknown amount of 20% juice, write as x(.2)
Since there will be a total of 6 quarts, the amount of 100% juice must be 6 quarts minus the amount of 20% juice, which I called 'x'.
Therefore, to model the amount of 100% juice, write it as (6-x)(1)
You can use these to make the equation x(.2)+(6-x)(1)=6(.8)
.2x+6-x=4.8
-0.8x+6=4.8
-0.8x=-1.2
x=1.5
This is the amount of 20% juice. To find the amount of 100%, subtract 1.5 from 6.
6-1.5=4.5. This is the amount of 100% juice to use.

Question 2: Find the flat cost and cost per page if 4 pages costs $5.36 and 7 pages costs $7.88.
Since we know that the flat cost is the same in both, we can model it with the variable 'y'
Also, since the cost per page is the same in both, we can model it with the variable 'x'
Therefore, we know that y+4x=5.36 and that y+7x=7.88
We can use the elimination method to solve for x. To do that, we must have one equation with y and one with -y.
Multiply the first equation by -1 to get -y-4x=-5.36
Eliminate the y's and add the other two
-y-4x=-5.36
y+7x=7.88
3x=2.52
Divide both sides by 3
x=.84
Then, plug x back into one of the equations
y+4(.84)=5.36
Simplify
y+3.36=5.36
Subtract 3.36 from both sides
y=2
Therefore, the flat rate $2 and the cost per page is $0.84