word problem

Question

A third grade class is making their own fruit punch for an after-school party. They want the punch to use 4% cherry juice and 8% white grape juice. How many gallons of each should be used to get a fruit punch that is 5% juice and containing a total of 2 gallons? Use c for cherry juice and g for the white grape juice.

 

(1) Set up a linear system of linear equations that models the situations. Use c for cherry juice and g for the white grape juice. (Convert any percents to decimals.)

 

(a)Equation 1
...................(A third grade class is making a total of 2 gallons of fruit punch.)
(b)Equation 2
................(They want the punch to use 4% cherry juice and 8% white grape juice. How many gallons of each should be used to get a fruit punch that is 5% juice and containing a total of 2 gallons?)

(2) Solve the system using substitution or elimination and write your answer to the problem in a complete sentence.
The class should use ............gallons of cherry juice and ..............gallons of grape juice

Answer 1

Hi Silvana,

 

Let c = gallons of cherry juice and let g = gallons of grape juice

 

Then c + g = 2

 

We need 5% juice after mixing 4% cherry with 8% grape

 

Convert % to decimal by moving the decimal point two places to the left

 

.04c + .08g = .05(c+g) = .05c + .05g

 

From the first equation, c = 2 - g

 

Now substitute that for c in the second equation

 

.04(2-g) + .08g = .05(2-g) + .05g

 

.08 - .04g + .08g = .1 - .05g + .05g

 

.08 + .04g = .1

 

.04g = .02

 

g= 0.5 gallons

 

then c = 1.5 gallons

 

This makes sense. . . you would expect more cherry juice since 4% is only a little less than 5% while 8% is a lot more than  5%.

 

Dan