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Question

Difficulty: EasyRatios, Rates, and Proportions

A beverage mixture is prepared by combining apple juice, orange juice, and grape juice in a ratio of 3:4:53 : 4 : 5 by volume. If a pitcher contains a total of 4848 fluid ounces of this mixture, how many fluid ounces of orange juice are in the pitcher?

  1. A
    1212 fluid ounces
  2. 1616 fluid ouncesAnswer
  3. C
    2020 fluid ounces
  4. D
    2424 fluid ounces
  5. E
    3636 fluid ounces

Answer

1616 fluid ounces
The ratio 3:4:53 : 4 : 5 indicates that the total mixture is divided into 3+4+5=123 + 4 + 5 = 12 equal parts. Orange juice accounts for 44 of these 1212 parts, representing 412=13\frac{4}{12} = \frac{1}{3} of the total volume. Taking 13\frac{1}{3} of 4848 fluid ounces gives 1616 fluid ounces.

Step-by-Step Solution

1
Calculate the total number of ratio parts.
Total parts = 3+4+5=123 + 4 + 5 = 12.
To find the fraction of each ingredient in the mixture, we must sum all parts of the ratio.
2
Determine the fraction of the total volume that represents orange juice.
Orange juice fraction = 412=13\frac{4}{12} = \frac{1}{3}.
Orange juice corresponds to 44 parts out of the 1212 total parts.
3
Multiply the orange juice fraction by the total volume.
13×48=16\frac{1}{3} \times 48 = 16 fluid ounces.
Multiplying the part-to-whole fraction by the total volume yields the exact volume of orange juice.

Key Concept

Part-to-Whole Ratio Relationships
Estimated Time:45s
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Topics

Ratios, Rates, and Proportions

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