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Difficulty: MediumRatios and Proportions

A supply convoy is distributing medical kits and rations to various outposts in a ratio of 2:72:7. If a particular outpost receives 5656 rations, how many medical kits should they receive?

Answer: 16 / 16 kits / 16 medical kits / sixteen

Answer

16
The correct amount is found by maintaining the ratio of 22 medical kits for every 77 rations. Since 5656 is 88 times as large as 77 (56÷7=856 \div 7 = 8), the number of medical kits must also be 88 times as large as 22. Multiplying the kit ratio component (22) by this scale factor (88) gives 1616 medical kits.

Step-by-Step Solution

1
Identify the given ratio and the known quantity.
Ratio of medical kits to rations is 2:72:7. The known quantity is 5656 rations.
Extracting the correct values and their relationship is required to set up the proportion.
2
Set up a proportion.
27=x56\frac{2}{7} = \frac{x}{56}
The ratio of kits to rations (2/72/7) must equal the ratio of actual kits (xx) to actual rations (5656).
3
Solve for the unknown value xx.
x=2×567=16x = \frac{2 \times 56}{7} = 16
Multiplying both sides by 5656 isolates xx, revealing the required number of medical kits.

Key Concept

Solving direct proportions using a scale factor or cross-multiplication

Alternative Method

Find the scale factor by dividing the actual number of rations by the ratio number for rations: 56÷7=856 \div 7 = 8. Then multiply the ratio number for medical kits by this scale factor: 2×8=162 \times 8 = 16.
Estimated Time:45s
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Topics

Ratios and Proportions

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