There were 6 more girls than boys in the auditorium. Excluding 9 boys, the number of boys was ²₃ of the number of girls. When another 6 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	6 more
Before	3 u	2 u + 9
Change	+ 6
After	3 u + 6	2 u + 9

Number of girls at first was 6 more than the number of boys. If another 6 boys entered the auditorium at first, the number of girls and boys at first would be the same.

3 u = 2 u + 9 + 6 
3 u - 2 u = 9 + 6

1 u = 15

Total number of girls in the end
= 3 u + 6
= 3 x 15 + 6
= 45 + 6
= 51

Total number of pupils in the end
= 3 u + 6 + 2 u + 9
= 5 u + 15
= 5 x 15 + 15
= 90

Fraction of the pupils who were girls in the end
= ⁵¹₉₀
= ¹⁷₃₀

Answer(s): ¹⁷₃₀