Problem 18 · 1999 AMC 8
Medium
Fractions, Decimals & Percents
percent-decreaseround-up
Cookies for a Crowd. The recipe makes a pan of 15 cookies, and only full recipes are made. Normally 108 students each eat 2 cookies, but a concert cuts attendance by 25%. How many recipes should Walter and Gretel make for the smaller party?
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Answer: E — 11 recipes.
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Hint 1 of 2
"Down 25%" means keep the other 75% — so multiply by ¾ instead of finding the 25% and subtracting. One step, not two.
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Hint 2 of 2
Get their cookies, divide by 15, then round UP to whole recipes (you can't bake a fraction of a pan).
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Approach: keep ¾ of the crowd → cookies → round up pans
- A 25% drop leaves ¾ of the students: ¾ × 108 = 81 students, eating 81 × 2 = 162 cookies.
- Recipes: 162 ÷ 15 = 10.8, round up to 11 full recipes.
- The handy reframe: "down 25%" → ×0.75 directly (and "up 25%" → ×1.25). And as always with whole pans, round up — 10 recipes (150 cookies) would leave 12 students cookieless.
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