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Question

Difficulty: MediumBasic Ratios

A quartermaster is organizing deployment cargo for four different platoons. Match each platoon's cargo inventory to the corresponding simplified ratio of the first listed item to the second listed item.

  • Platoon Alpha: 4545 cases of rations and 1515 cases of water3:13:1
  • Platoon Bravo: 2424 radio batteries and 3636 signal flares2:32:3
  • Platoon Charlie: 6060 sandbags and 100100 tent stakes3:53:5
  • Platoon Delta: 120120 standard rounds and 3030 tracer rounds4:14:1

Answer

Platoon Alpha matches to 3:13:1, Platoon Bravo matches to 2:32:3, Platoon Charlie matches to 3:53:5, and Platoon Delta matches to 4:14:1.
Each platoon's inventory forms a direct part-to-part ratio that can be simplified by dividing both quantities by their greatest common factor (GCF). Platoon Alpha's 45:1545:15 reduces to 3:13:1 (GCF is 1515). Platoon Bravo's 24:3624:36 reduces to 2:32:3 (GCF is 1212). Platoon Charlie's 60:10060:100 reduces to 3:53:5 (GCF is 2020). Platoon Delta's 120:30120:30 reduces to 4:14:1 (GCF is 3030).

Step-by-Step Solution

1
Determine the simplified ratio for Platoon Alpha (4545 rations to 1515 water).
The greatest common factor is 1515. Dividing both numbers by 1515 yields 3:13:1.
Simplifying the ratio reveals the baseline relationship between the two quantities.
2
Determine the simplified ratio for Platoon Bravo (2424 batteries to 3636 flares).
The greatest common factor is 1212. Dividing both numbers by 1212 yields 2:32:3.
Both terms must be reduced completely to find the correct matching equivalent.
3
Determine the simplified ratio for Platoon Charlie (6060 sandbags to 100100 stakes).
The greatest common factor is 2020. Dividing both numbers by 2020 yields 3:53:5.
Identifying the highest common divisor ensures the ratio is in its simplest form.
4
Determine the simplified ratio for Platoon Delta (120120 standard rounds to 3030 tracer rounds).
The greatest common factor is 3030. Dividing both numbers by 3030 yields 4:14:1.
Applying the same simplification principle resolves the final pairing.

Key Concept

Simplifying basic part-to-part ratios by identifying and dividing by the greatest common factor.
Estimated Time:1m 30s
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Topics

Basic Ratios

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