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All courses Math III · G-MG.2 40 of 55
Apply density concepts based on area and volume in modeling situations.

Find density by dividing a quantity by area

Problem
What is the population density for 120000 people over an area of 30 square miles?
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Hint

Use the density formula \(\text{density} = \frac{\text{population}}{\text{area}}\).

Population density tells how many people there are for each unit of area, so divide people by square miles or square kilometers.

Solution walkthrough

01

Write the density formula

\[\text{density}~=~\frac{\text{population}}\{\text{area}\}\]

Density compares how many people are spread over a certain amount of land.

02

Substitute the given values

\[\text{density}~=~\frac{120000}{30}\]

Use the population of \(120000\) and the area of \(30\) square miles.

03

Compute the quotient

\[\frac{120000}{30}~=~4000\]

Dividing gives the number of people for each square mile.

04

State the density with units

\[4000~\text{people}~\text{per}~\text{square}~\text{mile}\]

So the population density is \(4000\) people per square mile.

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Another way

  1. You can simplify first by dividing both numbers by 10: \(12000/3 = 4000\).

!

Common mistake

A common mistake is to divide the area by the population, which would reverse the meaning of density.