At the concert, there were 36 less girls than boys. After ¹₂ of the girls and ⁵₈ 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 concert at first.

	Girls	Boys	Less
Before	2x3 = 6 u	8x1 = 8 u	2 u
Change	- 1x3 = - 3 u	- 5x1 = - 5 u
After	1x3 = 3 u	3x1 = 3 u

Fraction of girls that remained
= 1 - ¹₂
= ¹₂

Fraction of boys that remained
= 1 - ⁵₈
= ³₈

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 3 is 3.

^1x3_2x3 Girls = ^3x1_8x1 Boys
³₆ Girls = ³₈ Boys

Total girls at first = 6 u
Total boys at first = 8 u

Number of less girls than boys at first
= 8 u - 6 u
= 2 u

2 u = 36

1 u = 36 ÷ 2 = 18

Number of girls at first
= 6 u
= 6 x 18
= 108

Answer(s): 108