There were 12 more girls than boys in the school hall. Excluding 7 boys, the number of boys was ³₄ of the number of girls. When another 10 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	12 more
Before	4 u	3 u + 7
Change	+ 10
After	4 u + 10	3 u + 7

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

4 u = 3 u + 7 + 12 
4 u - 3 u = 7 + 12

1 u = 19

Total number of girls in the end
= 4 u + 10
= 4 x 19 + 10
= 76 + 10
= 86

Total number of pupils in the end
= 4 u + 10 + 3 u + 7
= 7 u + 17
= 7 x 19 + 17
= 150

Fraction of the pupils who were girls in the end
= ⁸⁶₁₅₀
= ⁴³₇₅

Answer(s): ⁴³₇₅