Solving a percent mixture problem using a system of linear equations

Question

he Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 80% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 30 pints of a mixture that is pure fruit juice?

Answer 1

.9x + .65(30-x) = .8(30) = 24

.9x + 19.5 - .65x = 24

.25x = 4.5

x = 4.5/.25 = 450/25 = 18 pints of 90% mixed with 12 pints of 65% yield 30 pints of 80%

90 is within 10 of 80

65 is within 15 of 80

10/15 = 2/3 = 12/18 = 2/3