# 1995 AHSME Problems/Problem 5

## 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 $\Rightarrow \mathrm{(C)}$

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