A logistics unit packs 3 boxes of rations for every 4 boxes of water. If they pack 12 boxe… — Armed Services Vocational Aptitude Battery (ASVAB)

A logistics unit packs $3$ boxes of rations for every $4$ boxes of water. If they pack $12$ boxes of rations, how many boxes of water do they pack?

A
$9$
B
$13$
$16$ Answer
D
$28$

Answer

16

The ratio of rations to water is 3 to 4. Since the actual number of rations (12) is exactly 4 times the ratio number (3), the number of water boxes must also be 4 times its corresponding ratio number. Multiplying 4 by 4 yields 16 boxes of water.

Step-by-Step Solution

Set up the proportion comparing rations to water.

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

This establishes the mathematical relationship between the known ratio and the actual amounts.

Determine the scale factor for the rations.

12 \div 3 = 4

Finding how many times the base ratio was multiplied to get the actual number of rations.

Apply the scale factor to the water portion of the ratio.

4 \times 4 = 16

To maintain the proportion, both parts of the ratio must be multiplied by the same scale factor.

Key Concept

Solving basic proportions by finding and applying a scale factor.

Estimated Time:45s

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