There were 12 more boys than girls in the gymnasium. Excluding 7 girls, the number of girls was ³₄ of the number of boys. When another 10 boys joined, what fraction of the pupils were boys in the end? Give your answer in its simplest form.

	Boys	Girls
Comparing boys  and girls at first	12 more
Before	4 u	3 u + 7
Change	+ 10
After	4 u + 10	3 u + 7

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

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

1 u = 19

Total number of boys 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 boys in the end
= ⁸⁶₁₅₀
= ⁴³₇₅

Answer(s): ⁴³₇₅