Difference between revisions of "2018 AMC 8 Problems/Problem 1"

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You can set up a ratio: <math>\frac{1}{20}=\frac{x}{289}</math>. Cross multiplying, you get <math>20x=289</math>. You divide by 20 to get <math>x=14.45</math>. The closest integer is <math>\boxed{\textbf{(A)}14}</math>
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You can set up a ratio: <math>\frac{1}{20}=\frac{x}{289}</math>. Cross multiplying, you get <math>20x=289</math>. You divide by <math>20</math> on each side to get <math>x=14.45</math>. The closest integer is <math>\boxed{\textbf{(A)}14}</math>
  
 
==Solution 2==
 
==Solution 2==

Revision as of 13:25, 5 August 2019

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 $20$ on each side to get $x=14.45$. The closest integer is $\boxed{\textbf{(A)}14}$

Solution 2

Also, 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

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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