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.
