Question

The table below shows the total development costs and amount of land required for different
sized houses.
Size of house
1 Bedroom
2 Bedroom
3 Bedroom
4 Bedroom
5 Bedroom
Total development
cost
£210,000
£280,000
£345,000
£425,000
£495,000
Land area (square
metres)
50
70
84
94
118
People (per square
metre)
0.0400
Profit on a new build house is 27%.
0.0429
0.0476
0.0532
0.0508
Weston has a population of 14,300, which is expected to grow 4% every year for the next
three years.
Planning assumption: number of people living in a house = number of bedrooms + 1.
What is the largest number of people that can be housed on an area of land 200
metres long and 250 metres wide?
What is the largest number of people that can be housed on an area of land 200 metres long and 250 metres wide?

Answer 1

Calculating the land area:

$\bold{= (200\ m) \times (250\ m) = 50000\ m^2}$

Calculating the construction for the 1 Bedroom set:  

$= \bold{ (\frac{50000}{ \text{1 bedroom area}}) \times \text{(number of bedrooms + 1)}}\\\\ =\bold{ \frac{50000}{50} \times (1+1)} \\\\ = \bold{\frac{5000}{5} \times (2)} \\\\= \bold{2000\ people}$

Calculating the construction for the 2 Bedroom set:  

$= \bold{ (\frac{50000}{ \text{2 bedroom area}}) \times \text{(number of bedrooms + 1)}}\\\\ =\bold{ \frac{50000}{70} \times (2+1)} \\\\ = \bold{\frac{5000}{7} \times (3)} \\\\= \bold{2142 \ people}$

Calculating the construction for the 3 Bedroom set:  

$= \bold{ (\frac{50000}{ \text{3 bedroom area}}) \times \text{(number of bedrooms + 1)}}\\\\ =\bold{ \frac{50000}{84} \times (3+1)} \\\\ = \bold{\frac{50000}{84} \times (4)} \\\\= \bold{2380 \ people}$

Calculating the construction for the 4 Bedroom set:  

$= \bold{ (\frac{50000}{ \text{4 bedroom area}}) \times \text{(number of bedrooms + 1)}}\\\\ =\bold{ \frac{50000}{94} \times (4+1)} \\\\ = \bold{\frac{50000}{94} \times (5)} \\\\= \bold{2659 \ people}$

Calculating the construction for the 5 Bedroom set:  

$= \bold{ (\frac{50000}{ \text{5 bedroom area}}) \times \text{(number of bedrooms + 1)}}\\\\ =\bold{ \frac{50000}{118} \times (5+1)} \\\\ = \bold{\frac{50000}{118} \times (6)} \\\\= \bold{2542 \ people}$

In this scenario, the maximum number of persons accommodated is "2659", which would be the case for a 4-bedrooms set, therefore the final answer is "2659".

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