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.
[tex]\frac{1}{4}[/tex] of the pupils come from Elmswell
[tex]\frac{3}{5}[/tex] 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 = [tex]100x[/tex]
So, number of pupils that come from Elmswell = [tex]\frac{1}{4}[/tex] of 100x
OR
[tex]\dfrac{1}{4} \times 100x\\\Rightarrow 25x[/tex]
And, number of pupils that come from Haughley= [tex]\frac{3}{5}[/tex] of 100x
OR
[tex]\dfrac{3}{5} \times 100x\\\Rightarrow 60x[/tex]
Number of pupils that come from Woolpit = [tex]100x - 25x - 60x \Rightarrow 15x[/tex]
As per given statement:
[tex]15x = 102\\\Rightarrow x =6.8[/tex]
Number of pupils from Elmswell = 25x = 25 [tex]\times[/tex] 6.8 = 170
Number of pupils from Haughley = 60x = 60 [tex]\times[/tex] 6.8 = 408
Total number of pupils at the school = [tex]100x \Rightarrow 100 \times 6.8=680[/tex]
