2018 AMC 8 Problems/Problem 1: Difference between revisions

Revision as of 23:36, 18 June 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 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 (Vishal Vinjamuri)

2018 AMC 8 (Problems • Answer Key • Resources)
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

@@ Line 11: / Line 11: @@
 ==Solution 2==
-Alternatively, you can note that <math>20\cdot14</math> is <math>280</math>, and that <math>20\cdot15</math> is <math>300</math>. Since <math>289</math> is closer to <math>280</math>, the answer is <math>\boxed{\textbf{(A)}14}</math> ~ Mathscienceclass
+Also, you can note that <math>20\cdot14</math> is <math>280</math>, and that <math>20\cdot15</math> is <math>300</math>. Since <math>289</math> is closer to <math>280</math>, the answer is <math>\boxed{\textbf{(A)}14}</math> ~ Mathscienceclass
+(Vishal Vinjamuri)
 ==See Also==

Page

Toolbox

Search

2018 AMC 8 Problems/Problem 1: Difference between revisions

Revision as of 23:36, 18 June 2019

Contents

Problem 1

Solution 1

Solution 2

See Also