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	0.0429	0.0476	0.0532	0.0508
Profit on a new build house is 27%.

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?

To determine the largest number of people that can be housed on the given land (200 metres long and 250 metres wide), we need to break down the problem into several steps. Here's how we can approach it:

### Step 1: Calculate the total available land area.
The total area of land can be calculated by multiplying the length and the width:

\[
\text{Total area} = 200 \, \text{m} \times 250 \, \text{m} = 50,000 \, \text{square metres}
\]

### Step 2: Use the land area for each house size.
We are given the land area required for each house size:

| Size of House   | Land Area (square metres) |
|-----------------|---------------------------|
| 1 Bedroom       | 50                        |
| 2 Bedroom       | 70                        |
| 3 Bedroom       | 84                        |
| 4 Bedroom       | 94                        |
| 5 Bedroom       | 118                       |

### Step 3: Calculate the number of houses that can fit into the total land area.
We will calculate how many houses of each size can fit into the total available area of 50,000 square metres:

- **1 Bedroom**: 
\[
\text{Number of houses} = \frac{50,000}{50} = 1000 \, \text{houses}
\]

- **2 Bedroom**: 
\[
\text{Number of houses} = \frac{50,000}{70} \approx 714 \, \text{houses}
\]

- **3 Bedroom**: 
\[
\text{Number of houses} = \frac{50,000}{84} \approx 595 \, \text{houses}
\]

- **4 Bedroom**: 
\[
\text{Number of houses} = \frac{50,000}{94} \approx 532 \, \text{houses}
\]

- **5 Bedroom**: 
\[
\text{Number of houses} = \frac{50,000}{118} \approx 424 \, \text{houses}
\]

### Step 4: Calculate the number of people living in each house size.
The planning assumption is that the number of people living in a house = the number of bedrooms + 1. Thus, for each house size, the number of people per house is as follows:

- **1 Bedroom house**: \(1 + 1 = 2\) people
- **2 Bedroom house**: \(2 + 1 = 3\) people
- **3 Bedroom house**: \(3 + 1 = 4\) people
- **4 Bedroom house**: \(4 + 1 = 5\) people
- **5 Bedroom house**: \(5 + 1 = 6\) people

### Step 5: Calculate the maximum number of people that can be housed for each house size.
Now, we multiply the number of houses by the number of people per house:

- **1 Bedroom**: 
\[
\text{Total people} = 1000 \times 2 = 2000 \, \text{people}
\]

- **2 Bedroom**: 
\[
\text{Total people} = 714 \times 3 \approx 2142 \, \text{people}
\]

- **3 Bedroom**: 
\[
\text{Total people} = 595 \times 4 \approx 2380 \, \text{people}
\]

- **4 Bedroom**: 
\[
\text{Total people} = 532 \times 5 \approx 2660 \, \text{people}
\]

- **5 Bedroom**: 
\[
\text{Total people} = 424 \times 6 \approx 2544 \, \text{people}
\]

### Step 6: Conclusion
The largest number of people that can be housed on the available land is 2660, which corresponds to building **4 Bedroom houses**. Thus, building **532 houses with 4 bedrooms** will house **2660 people**.

---

Do you want more details on the calculations, or do you have any other questions?

### Related Questions:
1. How would the total development cost vary if all houses built were 3-bedroom homes?
2. How does the projected population growth affect future housing requirements for Weston?
3. What would the total profit be if the development sold only 5-bedroom houses?
4. How much more land would be required to house 3,000 people using only 2-bedroom houses?
5. What is the minimum land required to house the same population if only 5-bedroom houses are built?

### Tip:
When planning housing development, always consider not just the land but also infrastructure like roads and services, which can reduce the actual usable land.

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	0.0429	0.0476	0.0532	0.0508
Profit on a new build house is 27%.

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?

Find out how to calculate the maximum number of people that can be housed on a plot of land 200 metres long and 250 metres wide. Learn about land area calculation, house distribution, and population growth assumptions based on the size of the houses. This detailed guide is perfect for high school students studying practical applications of math.

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