Problem 17 · 1999 AMC 8
Medium
Arithmetic & Operations
round-upunit-conversion
Cookies for a Crowd. At a school, 108 students eat an average of 2 cookies apiece. The recipe makes a pan of 15 cookies and uses 2 eggs per pan, and only full recipes are made. Walter buys eggs by the half-dozen. How many half-dozens should he buy to make enough cookies?
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Answer: C — 5 half-dozens.
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Hint 1 of 2
Walk the chain of units: cookies needed → pans (round UP, since only whole recipes are baked) → eggs → half-dozens (round up again). The two round-ups are where this kind of problem traps people.
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Hint 2 of 2
When a quantity must come in whole units (pans, half-dozens), you always round UP — "enough" means never short, never exactly the leftover.
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Approach: unit-conversion chain, rounding up at every whole-unit step
- Cookies needed: 108 × 2 = 216. Pans: 216 ÷ 15 = 14.4, but you can't bake 0.4 of a pan, so round up to 15 pans.
- Eggs: 15 × 2 = 30. Half-dozens: 30 ÷ 6 = exactly 5.
- The reusable rule: whenever you buy/bake in fixed bundles, divide then round UP (ceiling) — rounding down would leave the crowd short. Here 14.4 → 15 pans is the make-or-break step; treating it as 14 undercounts the eggs.
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