There were 9 more boys than girls in the school hall. Excluding 5 girls, the number of girls was ²₃ of the number of boys. When another 9 boys joined, what fraction of the pupils were boys in the end? Give your answer in its simplest form.

	Boys	Girls
Comparing boys  and girls at first	9 more
Before	3 u	2 u + 5
Change	+ 9
After	3 u + 9	2 u + 5

Number of boys at first was 9 more than the number of girls. If another 9 girls entered the school hall at first, the number of boys and girls at first would be the same.

3 u = 2 u + 5 + 9 
3 u - 2 u = 5 + 9

1 u = 14

Total number of boys in the end
= 3 u + 9
= 3 x 14 + 9
= 42 + 9
= 51

Total number of pupils in the end
= 3 u + 9 + 2 u + 5
= 5 u + 14
= 5 x 14 + 14
= 84

Fraction of the pupils who were boys in the end
= ⁵¹₈₄
= ¹⁷₂₈

Answer(s): ¹⁷₂₈