Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 60% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% 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 65% pure fruit juice?

Answer 1

Make 2 equations from the question first
x is the number of pints for type 1
y is the number of pints for type 2

The equation
x + y = 120
60% x + 85% y = 65% (x + y)

Solve the equation
From the 2nd equation
0.6x + 0.85y = 0.65(x + y)
0.6x + 0.85y = 0.65x + 0.65y
0.85y - 0.65y = 0.65x - 0.6x
0.2y = 0.05x
y = 4x

From the 1st equation
x + y = 120
x + 4x = 120
5x = 120
x = 24

y = 4x
y = 96

The first type should be 24 pints, the second type should be 96 pints