Solving a percent mixture problem using a system of linear equations

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 70%

 pure fruit juice, and the second type is 95%

 pure fruit juice. The company is attempting to produce a fruit drink that contains 85%

 pure fruit juice. How many pints of each of the two existing types of drink must be used to make 60

 pints of a mixture that is 85%

 pure fruit juice?

Answer 1

.95x + .7(60-x) = .85(60)

.95x -.7x = .85(60) - .7(60)

.25x = .15(60) = 9

x = 9/.25 = 36 pints of 95%

60-x = 24 pints of 70%

85-70= 15

95-85 = 10

15/10 = 3/2 = 36/24