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Difficulty: MediumCalculating Percentages of Quantities

A quartermaster depot receives a shipment of 2,5002,500 emergency field rations. Upon inspection, 36%36\% of the rations are classified as vegetarian. Of these vegetarian rations, 15%15\% are also certified as gluten-free. How many gluten-free vegetarian rations are in the shipment?

  1. A
    375
  2. B
    525
  3. 135Answer
  4. D
    1,350

Answer

135
The correct answer is found by completing two sequential percentage calculations. First, find 36%36\% of the 2,5002,500 total rations (2,500×0.36=9002,500 \times 0.36 = 900). Then, find 15%15\% of those 900900 vegetarian rations (900×0.15=135900 \times 0.15 = 135).

Step-by-Step Solution

1
Calculate the number of vegetarian rations by finding 36%36\% of the total 2,5002,500 rations.
2,500×0.36=9002,500 \times 0.36 = 900 vegetarian rations.
The first percentage applies to the entire shipment of rations.
2
Calculate the number of gluten-free vegetarian rations by finding 15%15\% of the result from step 1.
900×0.15=135900 \times 0.15 = 135 gluten-free vegetarian rations.
The problem asks for 15%15\% 'Of these vegetarian rations', meaning the base for the second percentage is 900900, not 2,5002,500.

Key Concept

Calculating percentages of a specified subset in a multi-step word problem.
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Topics

Calculating Percentages of Quantities

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