There were 8 more boys than girls in the school hall. Excluding 9 girls, the number of girls was ³₄ of the number of boys. When another 10 boys joined, what fraction of the students were boys in the end? Give your answer in its simplest form.

	Boys	Girls
Comparing boys  and girls at first	8 more
Before	4 u	3 u + 9
Change	+ 10
After	4 u + 10	3 u + 9

Number of boys at first was 8 more than the number of girls. If another 8 girls entered the school hall at first, the number of boys and girls at first would be the same.

4 u = 3 u + 9 + 8 
4 u - 3 u = 9 + 8

1 u = 17

Total number of boys in the end
= 4 u + 10
= 4 x 17 + 10
= 68 + 10
= 78

Total number of students in the end
= 4 u + 10 + 3 u + 9
= 7 u + 19
= 7 x 17 + 19
= 138

Fraction of the students who were boys in the end
= ⁷⁸₁₃₈
= ¹³₂₃

Answer(s): ¹³₂₃