There were 4 more girls than boys in the auditorium. Excluding 12 boys, the number of boys was ²₃ of the number of girls. When another 7 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	4 more
Before	3 u	2 u + 12
Change	+ 7
After	3 u + 7	2 u + 12

Number of girls at first was 4 more than the number of boys. If another 4 boys entered the auditorium at first, the number of girls and boys at first would be the same.

3 u = 2 u + 12 + 4 
3 u - 2 u = 12 + 4

1 u = 16

Total number of girls in the end
= 3 u + 7
= 3 x 16 + 7
= 48 + 7
= 55

Total number of pupils in the end
= 3 u + 7 + 2 u + 12
= 5 u + 19
= 5 x 16 + 19
= 99

Fraction of the pupils who were girls in the end
= ⁵⁵₉₉
= ⁵₉

Answer(s): ⁵₉