At the musical performance, there were 81 less boys than girls. After ¹₂ of the boys and ⁵₇ of the girls had left the hall, there was an equal number of boys and girls that remained behind. Find the number of boys who were present at the musical performance at first.

	Boys	Girls	Less
Before	2x2 = 4 u	7x1 = 7 u	3 u
Change	- 1x2 = - 2 u	- 5x1 = - 5 u
After	1x2 = 2 u	2x1 = 2 u

Fraction of boys that remained
= 1 - ¹₂
= ¹₂

Fraction of girls that remained
= 1 - ⁵₇
= ²₇

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

^1x2_2x2 Boys = ^2x1_7x1 Girls
²₄ Boys = ²₇ Girls

Total boys at first = 4 u
Total girls at first = 7 u

Number of less boys than girls at first
= 7 u - 4 u
= 3 u

3 u = 81

1 u = 81 ÷ 3 = 27

Number of boys at first
= 4 u
= 4 x 27
= 108

Answer(s): 108