Question

Which has more​ people, County A with an area of 108 mi2 and a population density of 36 people km2 or County B with an area of 36 km2 and a population density of 108 people mi2​

Answer 1

County B

Explanation:

You want to know the greater population, given a county's area and population density:

• County A: 108 mi², 36 people/km²
• County B: 36 km², 108 people/mi²

Population

The population is the product of area and density:

`P_A=(108\text{ mi}^2)\frac{36\text{ people}}{\text{km}^2}=(108\cdot36\text{ people})\left(\frac{\text{mi}}{\text{km}}\right)^2\\\\P_B=(36\text{ km}^2)\frac{108\text{ people}}{\text{mi}^2}=(108\cdot36\text{ people})\left(\frac{\text{km}}{\text{mi}}\right)^2`

Comparison

To determine which product is greater, we simply need to know the relationship between kilometers and miles:

1 mi ≈ 1.609 km

The factor (km/mi) is greater, so the population of County B is greater.

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Additional comment

There are 1.609 km/mi, and about 0.6214 mi/km. The population of County B is about 6.7 times the population of County A.

County A has about 1501 people; County B has 10,070 people.