Problem 6 · 1985 AJHSME
Medium
Ratios, Rates & Proportions
sheets-per-cm
A stack of paper containing 500 sheets is 5 cm thick. Approximately how many sheets of this type of paper would there be in a stack 7.5 cm high?
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Answer: D — 750.
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Hint 1 of 2
Same paper means every sheet is the same thickness, so the number of sheets grows in lockstep with the height. 7.5 cm is one-and-a-half times 5 cm — what does that do to the sheet count?
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Hint 2 of 2
Find the 'unit rate' (sheets per single cm) and the rest is one multiplication. Unit rates turn any 'this much gives that much, so how much gives…?' question into a single step.
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Approach: scale up by the ratio of heights
- 500 sheets fill 5 cm, so the rate is 500 ⁄ 5 = 100 sheets per cm.
- A 7.5 cm stack holds 100 × 7.5 = 750 sheets.
- Sanity check: 7.5 cm is 1.5 × the 5 cm stack, so the count should be 1.5 × 500 = 750 — height and sheet count scale together because the paper is identical.
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