There were 12 more girls than boys in the auditorium. Excluding 3 boys, the number of boys was ²₃ of the number of girls. When another 3 girls joined, what fraction of the students were girls in the end? Give your answer in its simplest form.

	Girls	Boys
Comparing girls  and boys at first	12 more
Before	3 u	2 u + 3
Change	+ 3
After	3 u + 3	2 u + 3

Number of girls at first was 12 more than the number of boys. If another 12 boys entered the auditorium at first, the number of girls and boys at first would be the same.

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

1 u = 15

Total number of girls in the end
= 3 u + 3
= 3 x 15 + 3
= 45 + 3
= 48

Total number of students in the end
= 3 u + 3 + 2 u + 3
= 5 u + 6
= 5 x 15 + 6
= 81

Fraction of the students who were girls in the end
= ⁴⁸₈₁
= ¹⁶₂₇

Answer(s): ¹⁶₂₇