Question

A county is in the shape of a rectangle that is 40 miles by 30 miles and has a population of 50,000. What is the average number of people living in each square mile of the county? Round your answer to the nearest whole number.

42
357
31
56

Answer 1

To find the average number of people per square mile, we first need to determine the area of the county in square miles.

The area \( A \) of a rectangle can be calculated using the formula:

\[
A = \text{length} \times \text{width}
\]

In this case, the length is 40 miles, and the width is 30 miles:

\[
A = 40 \, \text{miles} \times 30 \, \text{miles} = 1200 \, \text{square miles}
\]

Next, we can find the average population density (people per square mile) by dividing the total population by the total area:

\[
\text{Population Density} = \frac{\text{Total Population}}{\text{Area}} = \frac{50000}{1200}
\]

Calculating this gives:

\[
\text{Population Density} \approx 41.67
\]

Rounding this to the nearest whole number gives us:

\[
42
\]

Thus, the average number of people living in each square mile of the county is **42**.