Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 60% pure fruit juice, and the second type is 75% pure fruit juice. The company is

attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two
existing types of drink must be used to make 120
pints of a mixture that is 70% pure fruit juice?

Answer 1

Explanation:

Let x = the 60% pure fruit juice

Let y = the 75% pure fruit juice

Set up two equations. Note that the larger of the two should be the 75% fruit juice because 70% is closer to 75%. The total amount of both % should be 120

60%x + 75%y = 70%120

x + y = 120

60x/100 + 75y/100 = 70/100 * 120

60x + 75y = 70*120

4x + 5y = 70 * 8

4x + 5y = 560

4x + 4y = 120*4

4x + 4y = 480

4x + 5y = 560

4x + 4y = 480 Subtract

y = 80

x + y = 120

x + 80 = 120 Subtract 80 from both sides

x = 120 - 80 Combine

x = 40

Notice that y>x as predicted.