Question

For her end of year party Adriana mixed 6 L of Brand A juice with 9 L of Brand B juice. Brand A contains 52% fruit and Brand B contains 12% fruit juice. What percent of the mixture is fruit juice?

A. 30%
B. 28%
C. 20%
D. 32%

Answer 1

B. 28%

Explanation:

You want to know the percent of the mixture that is fruit juice, if the mixture is 6 L of 52% juice and 9 L of 12% juice.

Juice

The total amount of juice in the 6+9 = 15 L of mix is ...

0.52·(6 L) +0.12(9 L) = 3.12 L +1.08 L = 4.2 L

Then the fraction of the mix that is fruit juice is ...

(4.2 L)/(15 L) = 0.28 = 28%

The percent of the mixture that is fruit juice is 28%, choice B.

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Additional comment

Effectively, the fraction is the weighted average of the fractions of the constituents. The weights are the number of liters of each constituent.

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