There were 11 more boys than girls in the school hall. Excluding 8 girls, the number of girls was ³₄ of the number of boys. When another 9 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	11 more
Before	4 u	3 u + 8
Change	+ 9
After	4 u + 9	3 u + 8

Number of boys at first was 11 more than the number of girls. If another 11 girls entered the school hall at first, the number of boys and girls at first would be the same.

4 u = 3 u + 8 + 11 
4 u - 3 u = 8 + 11

1 u = 19

Total number of boys in the end
= 4 u + 9
= 4 x 19 + 9
= 76 + 9
= 85

Total number of students in the end
= 4 u + 9 + 3 u + 8
= 7 u + 17
= 7 x 19 + 17
= 150

Fraction of the students who were boys in the end
= ⁸⁵₁₅₀
= ¹⁷₃₀

Answer(s): ¹⁷₃₀