There were 5 more girls than boys in the school hall. Excluding 3 boys, the number of boys was ³₄ of the number of girls. When another 7 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	5 more
Before	4 u	3 u + 3
Change	+ 7
After	4 u + 7	3 u + 3

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

4 u = 3 u + 3 + 5 
4 u - 3 u = 3 + 5

1 u = 8

Total number of girls in the end
= 4 u + 7
= 4 x 8 + 7
= 32 + 7
= 39

Total number of students in the end
= 4 u + 7 + 3 u + 3
= 7 u + 10
= 7 x 8 + 10
= 66

Fraction of the students who were girls in the end
= ³⁹₆₆
= ¹³₂₂

Answer(s): ¹³₂₂