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?

Question

Mathematics

Liana Madden

14 September, 09:06

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?

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Answers (1)

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Kennedi · 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