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Question

Difficulty: EasyRatio and Proportion Word Problems

A beverage recipe requires mixing orange juice and cranberry juice in a ratio of 4:14 : 1. If a caterer uses 1212 liters of orange juice, how many liters of cranberry juice must be added to maintain this ratio?

Answer: 3 liters

Answer

The caterer must add 3 liters of cranberry juice.
The ratio of orange juice to cranberry juice is 4:14:1. Since 1212 liters of orange juice represents 44 parts, each part equals 124=3\frac{12}{4} = 3 liters. Therefore, 11 part of cranberry juice equals 33 liters.

Step-by-Step Solution

1
Set up the ratio equation based on the recipe requirements.
Orange Juice : Cranberry Juice = 4:14 : 1
The problem states that for every 4 parts of orange juice, 1 part of cranberry juice is required.
2
Calculate the unknown amount of cranberry juice using the given quantity of orange juice.
Cranberry Juice = 124=3\frac{12}{4} = 3 liters
Since 12 liters represents 4 equal parts, dividing 12 by 4 yields the size of 1 part.

Key Concept

Direct Ratio and Proportion Scaling
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Topics

Ratio and Proportion Word Problems

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