There were 8 more girls than boys in the computer lab. Excluding 5 boys, the number of boys was ⁴₅ 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	8 more
Before	5 u	4 u + 5
Change	+ 7
After	5 u + 7	4 u + 5

Number of girls at first was 8 more than the number of boys. If another 8 boys entered the computer lab at first, the number of girls and boys at first would be the same.

5 u = 4 u + 5 + 8 
5 u - 4 u = 5 + 8

1 u = 13

Total number of girls in the end
= 5 u + 7
= 5 x 13 + 7
= 65 + 7
= 72

Total number of pupils in the end
= 5 u + 7 + 4 u + 5
= 9 u + 12
= 9 x 13 + 12
= 129

Fraction of the pupils who were girls in the end
= ⁷²₁₂₉
= ²⁴₄₃

Answer(s): ²⁴₄₃