Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1995 AHSME Problems/Problem 5"

(→‎See also)
 
(One intermediate revision by one other user not shown)
Line 6: Line 6:
  
 
==Solution==
 
==Solution==
−
The rectangular field is 3600 inches wide and 4800 inches long, so it has an area of 17280000 square inches. We multiply by three to account for the ants: 51840000, which is closes to 50 million <math>\Rightarrow \mathrm{(C)}</math>
+
The rectangular field is <math>300 \text{ feet} \cdot \frac{12 \text{ inches}}{1 \text{ foot}} =  3600 \text{ inches}</math> wide and <math>400 \text{ feet} \cdot \frac{12 \text{ inches}}{1 \text{ foot}} =  4800 \text{ inches}</math> inches long.
 +
 
 +
It has an area of <math>3.6\cdot 10^3 \cdot 4.8 \cdot 10^3 = 17.28 \cdot 10^6</math> square inches.  
 +
 
 +
We multiply by <math>3</math> to account for the ants to get approximately <math>50 \cdot 10^6</math>, which is <math>50</math> million <math>\Rightarrow \mathrm{(C)}</math>
  
 
==See also==
 
==See also==
 
{{AHSME box|year=1995|num-b=4|num-a=6}}
 
{{AHSME box|year=1995|num-b=4|num-a=6}}
 +
{{MAA Notice}}

Latest revision as of 12:58, 5 July 2013

Problem

A rectangular field is 300 feet wide and 400 feet long. Random sampling indicates that there are, on the average, three ants per square inch through out the field. [12 inches = 1 foot.] Of the following, the number that most closely approximates the number of ants in the field is


$\mathrm{(A) \ \text{500 thousand} } \qquad \mathrm{(B) \ \text{5 million} } \qquad \mathrm{(C) \ \text{50 million} } \qquad \mathrm{(D) \ \text{500 million} } \qquad \mathrm{(E) \ \text{5 billion} }$

Solution

The rectangular field is $300 \text{ feet} \cdot \frac{12 \text{ inches}}{1 \text{ foot}} = 3600 \text{ inches}$ wide and $400 \text{ feet} \cdot \frac{12 \text{ inches}}{1 \text{ foot}} = 4800 \text{ inches}$ inches long.

It has an area of $3.6\cdot 10^3 \cdot 4.8 \cdot 10^3 = 17.28 \cdot 10^6$ square inches.

We multiply by $3$ to account for the ants to get approximately $50 \cdot 10^6$, which is $50$ million $\Rightarrow \mathrm{(C)}$

See also

1995 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 4 		Followed by
Problem 6
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1995_AHSME_Problems/Problem_5&oldid=56441"