Problem 1 · 2018 AMC 8
Easy
Ratios, Rates & Proportions
ratioproportion
An amusement park has a collection of scale models, with a ratio of 1 : 20, of buildings and other sights from around the country. The height of the United States Capitol is 289 feet. What is the height in feet of its replica at this park, rounded to the nearest whole number?
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Answer: A — 14 feet.
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Hint 1 of 2
A scale of 1 : 20 means "the model is the smaller one." The real building is the big side (20), the replica is the small side (1) — so which way does 289 go, up or down?
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Hint 2 of 2
The technique: a ratio 1 : k shrinks the real size by dividing by k. Map the bigger number to the bigger part of the ratio so you never flip it by accident.
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Approach: divide by the scale factor
- The replica is the "1" side and the real Capitol is the "20" side, so the replica is 1/20 of 289 — smaller, which is the sanity check that we're dividing (a model should be tiny).
- 289 ÷ 20 = 14.45, which rounds to 14 feet.
- You'll see it again: any scale-model or map problem is just multiply or divide by the scale factor — the only decision is which way, and matching big-to-big settles it.
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