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Select all the counties with the same population density.

There are six counties listed in the table. Each county is generally in the shape of a rectangle.

\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{1}{|c|}{ County } & \multicolumn{1}{|c|}{ Length } & \multicolumn{1}{c|}{ Width } & \multicolumn{1}{c|}{ Population } \\
\hline Johnson & 16 miles & 19 miles & 7,600 \\
\hline Greene & 17 miles & 24 miles & 12,240 \\
\hline Robin & 28 miles & 30 miles & 23,520 \\
\hline Clark & 15 miles & 21 miles & 9,450 \\
\hline Wade & 22 miles & 23 miles & 15,180 \\
\hline Beaver & 20 miles & 20 miles & 11,600 \\
\hline
\end{tabular}

Johnson
Greene
Robin
Clark
Wade
Beaver



Answer :

GinnyAnswer
Let's solve the problem step-by-step.

### Step 1: Understand the Problem
We need to determine which counties have the same population density. Population density is defined as the number of people per unit area.

### Step 2: Calculate the Area of Each County
The area of each county can be calculated by multiplying its length by its width.

- Johnson: [tex]\( 16 \text{ miles} \times 19 \text{ miles} = 304 \text{ square miles} \)[/tex]
- Greene: [tex]\( 17 \text{ miles} \times 24 \text{ miles} = 408 \text{ square miles} \)[/tex]
- Robin: [tex]\( 28 \text{ miles} \times 30 \text{ miles} = 840 \text{ square miles} \)[/tex]
- Clark: [tex]\( 15 \text{ miles} \times 21 \text{ miles} = 315 \text{ square miles} \)[/tex]
- Wade: [tex]\( 22 \text{ miles} \times 23 \text{ miles} = 506 \text{ square miles} \)[/tex]
- Beaver: [tex]\( 20 \text{ miles} \times 20 \text{ miles} = 400 \text{ square miles} \)[/tex]

### Step 3: Calculate the Population Density for Each County
Population density is calculated by dividing the population by the area.

- Johnson: [tex]\( \frac{7600 \text{ people}}{304 \text{ square miles}} = 25 \text{ people per square mile} \)[/tex]
- Greene: [tex]\( \frac{12240 \text{ people}}{408 \text{ square miles}} = 30 \text{ people per square mile} \)[/tex]
- Robin: [tex]\( \frac{23520 \text{ people}}{840 \text{ square miles}} = 28 \text{ people per square mile} \)[/tex]
- Clark: [tex]\( \frac{9450 \text{ people}}{315 \text{ square miles}} = 30 \text{ people per square mile} \)[/tex]
- Wade: [tex]\( \frac{15180 \text{ people}}{506 \text{ square miles}} = 30 \text{ people per square mile} \)[/tex]
- Beaver: [tex]\( \frac{11600 \text{ people}}{400 \text{ square miles}} = 29 \text{ people per square mile} \)[/tex]

### Step 4: Identify Counties with the Same Population Density

Now we can gather the counties with the same population density:
- Greene, Clark, and Wade each have a population density of 30 people per square mile.

Thus, the counties with the same population density are Greene, Clark, and Wade.

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