There were 5 more girls than boys in the music room. Excluding 10 boys, the number of boys was ²₃ of the number of girls. When another 9 girls joined, what fraction of the pupils were girls in the end? Give your answer in its simplest form.

	Girls	Boys
Comparing girls  and boys at first	5 more
Before	3 u	2 u + 10
Change	+ 9
After	3 u + 9	2 u + 10

Number of girls at first was 5 more than the number of boys. If another 5 boys entered the music room at first, the number of girls and boys at first would be the same.

3 u = 2 u + 10 + 5 
3 u - 2 u = 10 + 5

1 u = 15

Total number of girls in the end
= 3 u + 9
= 3 x 15 + 9
= 45 + 9
= 54

Total number of pupils in the end
= 3 u + 9 + 2 u + 10
= 5 u + 19
= 5 x 15 + 19
= 94

Fraction of the pupils who were girls in the end
= ⁵⁴₉₄
= ²⁷₄₇

Answer(s): ²⁷₄₇