# 2018 AMC 8 Problems/Problem 1

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## Problem 1

An amusement park has a collection of scale models, with a ratio $1: 20$, 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 duplicate to the nearest whole number? $\textbf{(A) }14\qquad\textbf{(B) }15\qquad\textbf{(C) }16\qquad\textbf{(D) }18\qquad\textbf{(E) }20$

## Solution 1

You can set up a ratio: $\frac{1}{20}=\frac{x}{289}$. Cross multiplying, you get $20x=289$. You divide by $20$ on each side to get $x=14.45$. The closest integer is $\boxed{\textbf{(A)}14}$

## Solution 2

You can just do $\frac{289}{20}$ and round your answer to get $\boxed{\textbf{(A)}14}$. It is basically Solution 1 without the ratio calculation, which might not be necessary.

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 