There were 9 more girls than boys in the tuck shop. Excluding 10 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	9 more
Before	3 u	2 u + 10
Change	+ 6
After	3 u + 6	2 u + 10

Number of girls at first was 9 more than the number of boys. If another 9 boys entered the tuck shop at first, the number of girls and boys at first would be the same.

3 u = 2 u + 10 + 9 
3 u - 2 u = 10 + 9

1 u = 19

Total number of girls in the end
= 3 u + 6
= 3 x 19 + 6
= 57 + 6
= 63

Total number of pupils in the end
= 3 u + 6 + 2 u + 10
= 5 u + 16
= 5 x 19 + 16
= 111

Fraction of the pupils who were girls in the end
= ⁶³₁₁₁
= ²¹₃₇

Answer(s): ²¹₃₇