Difference between revisions of "2018 AMC 8 Problems/Problem 1"
(Created page with "==Problem 1== An amusement park has a collection of scale models, with ratio <math>1 : 20</math>, of buildings and other sights from around the country. The height of the Unit...") |
Hashtagmath (talk | contribs) |
||
(56 intermediate revisions by 26 users not shown) | |||
Line 1: | Line 1: | ||
− | ==Problem | + | ==Problem== |
− | An amusement park has a collection of scale models, with ratio <math>1 : 20</math>, 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 | + | An amusement park has a collection of scale models, with a ratio <math> 1: 20</math>, 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? |
<math>\textbf{(A) }14\qquad\textbf{(B) }15\qquad\textbf{(C) }16\qquad\textbf{(D) }18\qquad\textbf{(E) }20</math> | <math>\textbf{(A) }14\qquad\textbf{(B) }15\qquad\textbf{(C) }16\qquad\textbf{(D) }18\qquad\textbf{(E) }20</math> | ||
− | ==See | + | ==Solution 1== |
+ | |||
+ | |||
+ | You can see that since the ratios of real building's heights to the model building's height is <math>1:20</math>. We also know that the U.S Capitol is <math>289</math> feet in real life, so to find the height of the model, we divide by 20. That gives us <math>14.45</math> which rounds to 14. Therefore, to the nearest whole number, the duplicate is <math>\boxed{\textbf{(A)}14\text{ feet}}</math>. ~avamarora. | ||
+ | |||
+ | ==Solution 2== | ||
+ | |||
+ | |||
+ | We can compute <math>\frac{289}{20}</math> and round our answer to get <math>\boxed{\textbf{(A)}14}</math>. | ||
+ | It is basically Solution 1 without the ratio calculation. However, Solution 1 is referring further to the problem. | ||
+ | |||
+ | ==Solution 3== | ||
+ | We know that <math> 20 \cdot 14 = 280 ,</math> and that <math> 20 \cdot 15 = 300 .</math> These are the multiples of <math>20</math> around <math>289 ,</math> and the closest one of those is <math>280.</math> Therefore, the answer is <math> \dfrac {280} {20} = \boxed{\textbf{(A) }14} .</math> | ||
+ | |||
+ | ==See also== | ||
{{AMC8 box|year=2018|before=First Problem|num-a=2}} | {{AMC8 box|year=2018|before=First Problem|num-a=2}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 12:47, 18 January 2021
Problem
An amusement park has a collection of scale models, with a ratio , 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?
Solution 1
You can see that since the ratios of real building's heights to the model building's height is . We also know that the U.S Capitol is feet in real life, so to find the height of the model, we divide by 20. That gives us which rounds to 14. Therefore, to the nearest whole number, the duplicate is . ~avamarora.
Solution 2
We can compute and round our answer to get . It is basically Solution 1 without the ratio calculation. However, Solution 1 is referring further to the problem.
Solution 3
We know that and that These are the multiples of around and the closest one of those is Therefore, the answer is
See also
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.