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Difference between revisions of "1986 AHSME Problems/Problem 8"

(Fixed the problem statement and added a solution with explanation)
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==Solution==
 
==Solution==
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With about <math>230</math> million people and under <math>4</math> million square miles, there are about <math>60</math> people per square mile. Since a square mile is about <math>(5000 \text{ft})^{2} = 25</math> million square feet, that gives approximately <math>\frac{25}{60}</math> of a million square feet per person. <math>\frac{25}{60}</math> is approximately half, so the answer is approximately half a million, which is <math>\boxed{E}</math>.
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With about <math>230</math> million people and under <math>4</math> million square miles, there are about <math>60</math> people per square mile. Since a square mile is about <math>(5000 \ \text{ft})^{2} = 25</math> million square feet, that gives approximately <math>\frac{25}{60}</math> of a million square feet per person. <math>\frac{25}{60}</math> is approximately half, so the answer is approximately half a million, which is <math>\boxed{E}</math>.
  
 
== See also ==
 
== See also ==

Latest revision as of 17:23, 1 April 2018

Problem

The population of the United States in $1980$ was $226,504,825$. The area of the country is $3,615,122$ square miles. There are $(5280)^{2}$ square feet in one square mile. Which number below best approximates the average number of square feet per person?

$\textbf{(A)}\ 5,000\qquad \textbf{(B)}\ 10,000\qquad \textbf{(C)}\ 50,000\qquad \textbf{(D)}\ 100,000\qquad \textbf{(E)}\ 500,000$


Solution

With about $230$ million people and under $4$ million square miles, there are about $60$ people per square mile. Since a square mile is about $(5000 \ \text{ft})^{2} = 25$ million square feet, that gives approximately $\frac{25}{60}$ of a million square feet per person. $\frac{25}{60}$ is approximately half, so the answer is approximately half a million, which is $\boxed{E}$.

See also

1986 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 7 		Followed by
Problem 9
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 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

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