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Zorluk: OrtaRatios 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?

Cevap: 16 / 16 kits / 16 medical kits / sixteen

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Solving direct proportions using a scale factor or cross-multiplication

Alternatif Yöntem

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.
Tahmini Süre:45s
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Ratios and Proportions

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