A village has a population of 4200 and a population density of 700 people per km² - OCR - GCSE Maths - Question 20 - 2017 - Paper 1

Next, we add the population of the village to the population of the estate:

$\text{Total Population} = \text{Population}_{\text{village}} + \text{Population}_{\text{estate}}$

Substituting in the values we have:

$\text{Total Population} = 4200 + 1600 = 5800 \text{ people}$

Now, we need to find the total area by combining the area of the village and the estate. Since the area of the village is calculated by its population divided by its density:

$\text{Area}_{\text{village}} = \frac{\text{Population}_{\text{village}}}{\text{Population Density}_{\text{village}}} = \frac{4200}{700} = 6 \text{ km}^2$

Then we add the area of the estate:

$\text{Total Area} = \text{Area}_{\text{village}} + \text{Area}_{\text{estate}} = 6 + 2 = 8 \text{ km}^2$

Finally, we calculate the overall population density using the total population and total area:

$\text{Population Density} = \frac{\text{Total Population}}{\text{Total Area}} = \frac{5800 \text{ people}}{8 \text{ km}^2} = 725 \text{ people/km}^2$