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 55%

 pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 90 pints of a mixture that is 75% pure fruit juice?

First fruit drink:

Second fruit drink:

Answer 1

x pints of the first, y of the second

x + y = 90

(0.55 x + 0.80y) / 90 = 0.75

55x + 80 y = 6750

x + y = 90

y = 90 - x

55x + 80 (90-x) = 6750

-25x + 7200 = 6750

-25x = -450

x = 18

y = 72