2018 AMC 8 Problems/Problem 1

Problem

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 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 ratio 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. Therefore, to the nearest whole number, the duplicate is $\boxed{\textbf{(A) }14\text{ feet}}$. ~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 $\dfrac {280} {20} = \boxed{\textbf{(A) }14} .$

Video Solution

https://youtu.be/rRaMWpifJJE

~savannahsolver

See also

2018 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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