A recipe for fruit punch calls for orange juice and cranberry juice to be mixed in a ratio… — ACT

A recipe for fruit punch calls for orange juice and cranberry juice to be mixed in a ratio of $3:4$ . If a chef uses $12$ cups of orange juice, how many cups of cranberry juice should be used?

A
4
B
9
C
13
16Answer
E
28

Answer

16 cups

Since the ratio of orange juice to cranberry juice is 3 to 4, we can set up the proportion 3/4 = 12/x, where x is the amount of cranberry juice. Solving for x yields 16 cups.

Step-by-Step Solution

Set up a proportion based on the ratio of orange juice to cranberry juice.

\frac{3}{4} = \frac{12}{x}

where

x

represents the number of cups of cranberry juice.

The ratio of orange juice to cranberry juice is constant at 3 to 4.

Solve the proportion for

x

by cross-multiplying.

3x = 12 \times 4

3x = 48

Cross-multiplication is a standard method to solve proportions.

Divide both sides by 3 to isolate

x

x = 16

Isolating the variable gives the required amount of cranberry juice.

Key Concept

Solving a part-to-part ratio problem using proportions.

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