Question

A school gets a big donation and adds ten rooms. This reduces the average numbe of pupils per room by ten. After two months, a storm badly damages five rooms forcing the school to close them. This causes the average number of pupils per room to increase by four. The number of pupils at the school remains constant throughou this time. How many pupils are at the school? Justify your answer with working.​

Answer 1

600 pupils

Explanation:

Let x represent the number of pupils at the school.

Let y represent the initial number of rooms in the school.

The average before the donation is:

1. x/y

The average after the donation is:

2. x/(y+10)

Set an equation between those two averages (the second line is 10 less than the first):

x/(y+10) + 10 = x/y

The average after the storm is:

x/(y+10-5)

3. x/(y+5)

Create another equation from the second line and third line:

x/(y+5) - 4 = x/(y+10)

We now have two equations and two variables

1. x/(y+10) + 10 = x/y

2. x/(y+5) - 4 = x/(y+10)

Solving them leads to x being 600 and y being 20.

Therefore there are 600 pupils at the school.