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Difficulty: MediumDividing in a Ratio

A quartermaster is allocating 2,1002,100 yards of heavy-duty canvas to manufacture temporary shelters, cot covers, and equipment tarps. The canvas is divided among these three projects in a ratio of 6:5:36:5:3, respectively. What is the difference, in yards, between the amount of canvas allocated for the temporary shelters and the amount allocated for the equipment tarps?

Answer: 450 yards

Answer

450
The correct answer is found by determining that the total ratio consists of 14 parts, meaning each part represents 150 yards (2100 / 14). The difference between the shelters (6 parts) and tarps (3 parts) is 3 parts, which equals 450 yards (3 * 150).

Step-by-Step Solution

1
Calculate the total number of parts in the ratio.
6+5+3=146 + 5 + 3 = 14 total parts.
To divide the total amount of canvas proportionally, we first need to determine the total number of equal parts.
2
Determine the value of a single part.
2,100÷14=1502,100 \div 14 = 150 yards per part.
Dividing the total yards by the total parts gives the amount of canvas for each ratio unit.
3
Calculate the difference in ratio parts between the shelters and the tarps.
66 parts (shelters) - 33 parts (tarps) = 33 parts difference.
We need the difference between the two allocations. Finding the difference in parts directly is the most efficient method.
4
Calculate the difference in yards.
3×150=4503 \times 150 = 450 yards.
Multiplying the difference in ratio parts by the value of a single part yields the final answer.

Key Concept

Dividing a total quantity into a given ratio by finding the value of a single part.
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Topics

Dividing in a Ratio

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