SOLUTION: 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 produc
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Question 1199770: 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 75% 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 75% pure fruit juice? Answer by greenestamps(13200) (Show Source):
(1) A typical setup for solving using formal algebra....
let x = number of pints of 60% pure juice
then 150-x = number of pints of 85% pure juice
x pints of 60%, plus (150-x) pints of 85%, yields 150 pints of 75%:
I leave it to you to solve that equation to find the answer to the problem.
(2) A quick and easy informal method, if formal algebra is not required....
Observe/calculate (using a number line, if it helps) that 75% is 15/25 = 3/5 of the way from 60% to 85%. That means 3/5 of the mixture is the 85% pure juice.
ANSWER: 3/5 of 150 pints, or 90 pints, is the 85% pure juice; the other 60 pints are the 60% pure juice
