At the musical performance, there were 65 less girls than boys. After ¹₂ of the girls and ⁷₉ of the boys had left the hall, there was an equal number of girls and boys that remained behind. Find the number of girls who were present at the musical performance at first.

	Girls	Boys	Less
Before	2x2 = 4 u	9x1 = 9 u	5 u
Change	- 1x2 = - 2 u	- 7x1 = - 7 u
After	1x2 = 2 u	2x1 = 2 u

Fraction of girls that remained
= 1 - ¹₂
= ¹₂

Fraction of boys that remained
= 1 - ⁷₉
= ²₉

The number of girls and boys in the end is the same. Make the number of girls and boys in the end the same. LCM  of 1 and 2 is 2.

^1x2_2x2 Girls = ^2x1_9x1 Boys
²₄ Girls = ²₉ Boys

Total girls at first = 4 u
Total boys at first = 9 u

Number of less girls than boys at first
= 9 u - 4 u
= 5 u

5 u = 65

1 u = 65 ÷ 5 = 13

Number of girls at first
= 4 u
= 4 x 13
= 52

Answer(s): 52