Question

20 pts plus a mark!! The Royal Fruit Company produces two types of fruit drinks. The first type is 80% pure fruit juice, and the second type is 100% pure fruit juice. The company is attempting to produce a fruit drink that contains 95% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 220 pints of a mixture that is 95% pure fruit juice?

Answer 1

• 165 pints 100% juice
• 55 pints 80% juice

Explanation:

Once you see how the solution works, it becomes possible to write down the answer to a problem like this with very little computation.

Let x represent the quantity of the higher-percentage juice that must be used. The quantity of pure fruit juice in the mix is ...

80%(220 -x) +100%(x) = 95%(220)

(100% -80%)x = 220(95% -80%) . . . . . subtract 80%(220), collect terms

x = 220(95% -80%)/(100% -80%)

Take a good look at this. The fraction of high-percentage juice in the mix is equal to the ratio of the difference of mix% and low-percent to the difference of high-percent and low-percent.

x = 220(3/4) = 165 . . . . quantity of 100% pure fruit juice (pints)

220 -x = 55 . . . . . . . . . . quantity of 80% pure fruit juice (pints)

To make 220 pints of 95% juice, 165 pints of 100% juice and 55 pints of 80% juice must be used.