Question

10%

A village has an area of 6 km’ and a population density of 600 people per km².
An estate situated next to the village has a population of 800 and a population
density of 400 people per km².
Work out the population density, in people per km², for the village alad
the estate together.
+
[2]

Answer 1

The population density for the village and estate together is 400 people/km².

Step-by-step explanation:

To find the population density for the village and estate together, we need to calculate the total population and the total area.

The village has an area of 6 km² and a population density of 600 people/km², so the total population is -

6 km² * 600 people/km² = 3600 people.

The estate has a population of 800 people and a population density of 400 people/km², so the total area is -

800 people / 400 people/km² = 2 km².

Therefore, the population density for the village and estate together is -

3600 people / (6 km² + 2 km²)

= 400 people/km².

Answer 2

The population density for the village and the estate together is 112.5 people per square kilometer.

Step-by-step explanation:

The statement is incorrectly written. Correct form is described below:

A village has an area of 6 square kilometers and a population density of 600 people per square kilometer. An estate stituated next to the village has a population of 800 and a population density of 400 people per square kilometer. Work out the population density, in people per square kilometer, for the village and the state together.

Dimensionally speaking, the population density of the village and the estate together (
`r`), measured in people per square kilometer, is defined by this expression:

`r = (n_(V)+n_(E))/(A_(V)+A_(E))` (1)

Where:

`n_(V)`,
`n_(E)` - Population of the village and the estate, measured in people.

`A_(V)`,
`A_(E)` - Area of the village and the estate, measured in square kilometers.

First, we find the population of the village:

`n_(V) = (600\,(p)/(km^(2)) )/(6\,km^(2))`

`n_(V) = 100\,p`

Then, we determine the area of the estate:

`A_(E) = (800\,p)/(400\,(p)/(km^(2)) )`

`A_(E) = 2\,km^(2)`

If we know that
`n_(V) = 100\,p`,
`n_(E) = 800\,p`,
`A_(V) = 6\,km^(2)` and
`A_(E) = 2\,km^(2)`, then the population density of the village and the estate together is:

`r = (100\,p+800\,p)/(6\,km^(2)+2\,km^(2))`

`r = 112.5\,(p)/(km^(2))`

The population density for the village and the estate together is 112.5 people per square kilometer.