Problem 3 · 2004 AMC 8
Easy
Ratios, Rates & Proportions
proportion
Twelve friends met for dinner at Oscar's Overstuffed Oyster House, and each ordered one meal. The portions were so large, there was enough food for 18 people. If they shared, how many meals should they have ordered to have just enough food for the 12 of them?
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Answer: A — 8 meals.
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Hint 1 of 2
The 12 friends are a distraction — the real fact is 'this much food'. How many people does a single meal actually feed?
Still stuck? Show hint 2 →
Hint 2 of 2
This is a capacity / unit-rate setup: turn the deal into 'people fed per meal', then ask how many meals reach your target. Same skill as 'miles per gallon' or 'words per minute'.
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Approach: people-fed-per-meal rate
- Find what one meal is worth: 12 meals stretched to feed 18 people means each meal feeds 18 ÷ 12 = 1.5 people. That's the insight — the meals are 50% bigger than one person needs.
- To feed exactly 12 people: 12 ÷ 1.5 = 8 meals.
- Sanity check: meals feed more than one person each, so we should need fewer than 12 meals — and 8 < 12. Good.
Another way — ratio scaling:
- Meals-to-people stays fixed at 12 : 18, which reduces to 2 : 3.
- Scale the 'people' side down to 12: that's 12 / 3 = 4 groups, so meals = 2 × 4 = 8.
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