2018 AMC 8 Problems/Problem 1

Problem 1

An amusement park has a collection of scale models, with 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 replica 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 to get $x=14.45$ . The closest integer is $\boxed{\textbf{(A)}14}$

Solution 2

Alternatively, you can note that $20\cdot14$ is $280$ , and that $20\cdot15$ is $300$ . Since $289$ is closer to $280$ , the answer is $\boxed{\textbf{(A)}14}$ ~ Mathscienceclass

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

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2018 AMC 8 Problems/Problem 1

Contents

Problem 1

Solution 1

Solution 2

See Also