System of Linear equations

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 40% pure fruit juice, and the second type is 65% pure fruit juice. The company is attempting to produce a fruit drink that contains 55% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 55% pure fruit juice?

First Fruit drink

Second fruit drink

Answer 1

.4x + .65(50-x) = .55(50)

.4x + 32.5 - .65x = 27.5

.25x = 5

x = 20 pints of 40%

50-x = 30 pints of 65%

65-55 = 10

55-40 = 15

15/10 = 1.5 = 30/20

.40(20) =8

.65(30) = 19.5

55(50) = 27.5

8+19.5=27.5