Word Problem add 70% and 20% to get 55% mixture

Question

A company produces 1 juice that contains 20% real fruit juice. They produce another that is 70% real fruit juice.
How many pints of each juice would be needed to produce 40 pints of juice that contains 55% real fruit juice?

Answer 1

 

 

Let x= 1st juice

    y = 2nd juice

 

 

.7x+.2y=.55(x+y)

.7x+.2y=.55x+.55y

.15x-.35y=0

 

x+y=40

.15x-.35y=0

 

Multiply the 2nd equation by 100 to get rid of the decimals.

 

100[.15x-.35y=0]            15x-35y=0

15x-35y=0         15x-35y=0        15x-35y=0

  x+y=40         -15[x+y=40]      -15x-15y=-600

                                               ----------------

                                                       -50y=-600

                                                            y=12

 

Substitute back into 1st equation

 

x+y=40

x+12=40

x=28

 

ANSWER:  28 of the 1st and 12 of the 2nd