Problem 19 · 1999 AMC 8
Medium
Arithmetic & Operations
round-upunit-conversion
Cookies for a Crowd. The recipe makes a pan of 15 cookies using 3 tablespoons of butter, and only full recipes are made. Walter and Gretel must supply 216 cookies. There are 8 tablespoons in a stick of butter. How many sticks of butter are needed?
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Answer: B — 6 sticks.
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Hint 1 of 2
Same chain as before: cookies → pans (round up) → tablespoons → sticks (round up). Two whole-unit steps means two round-ups.
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Hint 2 of 2
Don't round the pans down: 216 ÷ 15 isn't a whole number, so it takes 15 full pans — and that drives the butter total.
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Approach: cookies → pans → tablespoons → sticks, rounding up each whole-unit step
- Pans for 216 cookies: 216 ÷ 15 = 14.4 → round up to 15 pans. Butter: 15 × 3 = 45 tablespoons.
- Sticks: 45 ÷ 8 = 5.625 → round up to 6 sticks.
- The recurring trap: rounding 14.4 down to 14 pans gives 42 tbsp and the wrong stick count. Whole supplies always round UP — and a leftover ⅜ of a stick is fine, the problem even says "some butter may be left over."
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