Problem 1 · 2012 AMC 8
Easy
Ratios, Rates & Proportions
proportion
Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighborhood picnic?
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Answer: E — 9 pounds.
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Hint 1 of 2
Don't reach for a formula — just compare the two orders. How many times bigger is 24 hamburgers than 8?
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Hint 2 of 2
This is scaling a recipe: if everything in the recipe grows by the same factor, the meat grows by that factor too.
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Approach: scale the recipe by the same factor
- Notice 24 is exactly 3 batches of 8 (24 / 8 = 3) — she's making the same recipe 3 times over.
- So everything triples, including the meat: 3 × 3 = 9 pounds.
- Why this works & transfers: in any rate/recipe problem, scale both sides by the same factor — spotting the whole-number multiplier (here, ×3) beats setting up a cross-multiplication.
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