Answer:
<em>680</em>
Step-by-step explanation:
Given that:
All the pupils at a primary school come from one of three villages: Elmswell, Haughley or Woolpit.
of the pupils come from Elmswell
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](https://tex.z-dn.net/?f=100x)
So, number of pupils that come from Elmswell =
of 100x
OR
![\dfrac{1}{4} \times 100x\\\Rightarrow 25x](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D%20%5Ctimes%20100x%5C%5C%5CRightarrow%2025x)
And, number of pupils that come from Haughley=
of 100x
OR
![\dfrac{3}{5} \times 100x\\\Rightarrow 60x](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B5%7D%20%5Ctimes%20100x%5C%5C%5CRightarrow%2060x)
Number of pupils that come from Woolpit = ![100x - 25x - 60x \Rightarrow 15x](https://tex.z-dn.net/?f=100x%20-%2025x%20-%2060x%20%5CRightarrow%2015x)
As per given statement:
![15x = 102\\\Rightarrow x =6.8](https://tex.z-dn.net/?f=15x%20%3D%20102%5C%5C%5CRightarrow%20x%20%3D6.8)
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 \times 6.8=680](https://tex.z-dn.net/?f=100x%20%5CRightarrow%20100%20%5Ctimes%206.8%3D680)