Question

The Royal Fruit Company produces two types of fruit drinks. The first type is

35%
pure fruit juice, and the second type is
60%
pure fruit juice. The company is attempting to produce a fruit drink that contains
40%
pure fruit juice. How many pints of each of the two existing types of drink must be used to make
150
pints of a mixture that is
40%
pure fruit juice?

Answer 1

• 120 pints of 35% juice

• 30 pints of 60% juice

Explanation:

You are asked to find the quantity of each kind of juice, and you are told the total quantity required. It is generally convenient to choose a variable to represent the quantity that makes the greatest contribution to the mix. Here, that is the 60% juice, so we can let q represent the quantity (in pints) required of that.

Then (150-q) is the quantity required of 35% juice.

The total amount of juice in the mix is ...

0.60q + 0.35(150 -q) = 0.40·150

0.25q = 150(0.40 -0.35) . . . . simplify, subtract 0.35·150

q = 150(0.05/0.25) = 30 . . . . pints of 60% juice

150-q = 120 . . . . . . . . . . . . . . . pints of 35% juice

120 pints of 35% juice and 30 pints of 60% juice are required to make 150 pints of 40% juice.