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

Answer:

680

Step-by-step explanation:

Given that:

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

$\frac{1}{4}$ of the pupils come from Elmswell

$\frac{3}{5}$ 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 = $\frac{1}{4}$ of 100x

OR

$\dfrac{1}{4} \times 100x\\\Rightarrow 25x$

And, number of pupils that come from Haughley= $\frac{3}{5}$ of 100x

OR

$\dfrac{3}{5} \times 100x\\\Rightarrow 60x$

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 $\times$ 6.8 = 170

Number of pupils from Haughley = 60x = 60 $\times$ 6.8 = 408

Total number of pupils at the school = $100x \Rightarrow 100 \times 6.8=680$