Problem 2 · 2009 AMC 8
Easy
Ratios, Rates & Proportions
proportion
On average, for every 4 sports cars sold at the local dealership, 7 sedans are sold. The dealership predicts that it will sell 28 sports cars next month. How many sedans does it expect to sell?
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Answer: D — 49 sedans.
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Hint 1 of 2
Think of the cars in repeating BATCHES: every batch is 4 sports cars + 7 sedans. The whole question is just 'how many batches?'
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Hint 2 of 2
Find the scale factor (what turns 4 into 28), then apply that SAME factor to 7. This is what 'keeping a ratio' means.
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Approach: scale the ratio by a single factor
- How many batches of 4 sports cars make 28? 28 ÷ 4 = 7 batches.
- Each batch also has 7 sedans, so 7 batches give 7 × 7 = 49 sedans.
- You'll see it again as: any 'A is to B' ratio scaled to a new amount — find the multiplier on one quantity, reuse it on the other. No cross-multiplying needed when the numbers divide nicely.
Another way — proportion (cross-multiply):
- Set 4/7 = 28/x. Cross-multiply: 4x = 7 × 28 = 196.
- x = 49. (Slower here, but the go-to when the scale factor isn't a whole number.)
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