2018 AMC 8 Problems/Problem 1

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 see that since the ratios of real building's heights to the model building's height is 1:20. We also know that the U.S Capitol is 289 feet in real life so to find the height of the model, we divide by 20. That gives us 14.45 which rounds to 14. So the answer is $\boxed{\textbf{(A)}14}$ . ~avamarora.

Solution 2

We can compute $\frac{289}{20}$ and round our answer to get $\boxed{\textbf{(A)}14}$ . It is basically Solution 1 without the ratio calculation. However, Solution 1 is referring further to the problem.

Solution 3

We know that $20 \cdot 14 = 280 ,$ and that $20 \cdot 15 = 300 .$ These are the multiples of $20$ around $289 ,$ and the closest one of those is $280.$ Therefore, the answer is $\dfrac {280} {14} = \boxed{\textbf{(A) }14} .$

2018 AMC 8 (Problems • Answer Key • Resources)
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All AJHSME/AMC 8 Problems and Solutions

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

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2018 AMC 8 Problems/Problem 1

Contents

Problem 1

Solution 1

Solution 2

Solution 3

See also