A logistics officer needs to distribute 150 tactical backpacks between two infantry squads… — Armed Services Vocational Aptitude Battery (ASVAB)

A logistics officer needs to distribute $150$ tactical backpacks between two infantry squads in a ratio of $2:3$ . How many backpacks will the squad with the smaller share receive?

Answer: 60 backpacks

Answer

To solve the problem, we first determine that the total ratio consists of

5

parts (

2 + 3

). Dividing the

150

total backpacks by

5

parts gives us

30

backpacks for every single part. Because the question asks for the squad with the smaller share, we multiply the

30

backpacks by the smaller ratio number (

2

), which results in

60

backpacks.

Step-by-Step Solution

Calculate the total number of parts in the ratio by adding the given values.

2 + 3 = 5

total parts.

This establishes the total number of equal shares the backpacks will be divided into.

Determine the number of backpacks in a single part by dividing the total amount by the total parts.

150 \div 5 = 30

backpacks per part.

Finding the unit value allows us to calculate any specific share in the proportion.

Calculate the smaller share by multiplying the unit value by the smaller number in the ratio.

30 \times 2 = 60

backpacks.

The question asks for the smaller share, which corresponds to the

2

parts in the

2:3

ratio.

Key Concept

Dividing a total quantity into a given ratio

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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