Question

All the pupils at a primary school come from one of three villages: Elmswell, Haughley or Woolpit. 1/4 of the pupils come from Elmswell. 3/5 of the pupils come from Haughley. 102 pupils come from Woolpit. How many pupils are there in total at the school?

Answer 1

680

Explanation:

Given that:

All the pupils at a primary school come from one of three villages: Elmswell, Haughley or Woolpit.

`(1)/(4)` of the pupils come from Elmswell

`(3)/(5)` of the pupils come from Haughley

102 pupils come from Woolpit.

To find:

Total number of pupils in the school.

Solution:

Let total number of pupils =
`100x`

So, number of pupils that come from Elmswell =
`(1)/(4)` of 100x

OR

`(1)/(4) * 100x\\\Rightarrow 25x`

And, number of pupils that come from Haughley=
`(3)/(5)` of 100x

OR

`(3)/(5) * 100x\\\Rightarrow 60x`

Number of pupils that come from Woolpit =
`100x - 25x - 60x \Rightarrow 15x`

As per given statement:

`15x = 102\\\Rightarrow x =6.8`

Number of pupils from Elmswell = 25x = 25
`*` 6.8 = 170

Number of pupils from Haughley = 60x = 60
`*` 6.8 = 408

Total number of pupils at the school =
`100x \Rightarrow 100 * 6.8=680`