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Difficulty: EasyRatios and Proportions

A military base assigns personnel to guard duty and patrol duty in a ratio of 5:25:2. If there are 4040 personnel assigned to guard duty, what is the total number of personnel assigned to both duties combined?

  1. A
    16
  2. 56Answer
  3. C
    100
  4. D
    140

Answer

The total number of personnel assigned to both duties is 56.
The correct answer accurately determines that 5 parts equal 40 personnel, meaning 1 part is equal to 8 personnel. The total number of personnel represents 7 parts in total (5 + 2). Multiplying 7 total parts by 8 personnel per part results in 56 total personnel.

Step-by-Step Solution

1
Determine the value of one part of the ratio.
1 part = 8 personnel
The ratio of guard to patrol duty is 5:2, meaning 5 parts correspond to the 40 personnel on guard duty. Dividing 40 by 5 gives the value of a single part.
2
Calculate the total number of parts in the given ratio.
Total parts = 7
The total personnel is the sum of guard duty parts (5) and patrol duty parts (2).
3
Multiply the total parts by the value of one part.
7 × 8 = 56 personnel
Multiplying the total number of parts by the personnel value of each individual part gives the combined total.

Key Concept

Solving part-to-whole ratio problems by determining the value of a single unit part.
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Topics

Ratios and Proportions

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