At the musical performance, there were 70 less boys than girls. After ¹₃ of the boys and ³₄ 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	3x1 = 3 u	4x2 = 8 u	5 u
Change	- 1x1 = - 1 u	- 3x2 = - 6 u
After	2x1 = 2 u	1x2 = 2 u

Fraction of boys that remained
= 1 - ¹₃
= ²₃

Fraction of girls that remained
= 1 - ³₄
= ¹₄

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 2 and 1 is 2.

^2x1_3x1 Boys = ^1x2_4x2 Girls
²₃ Boys = ²₈ Girls

Total boys at first = 3 u
Total girls at first = 8 u

Number of less boys than girls at first
= 8 u - 3 u
= 5 u

5 u = 70

1 u = 70 ÷ 5 = 14

Number of boys at first
= 3 u
= 3 x 14
= 42

Answer(s): 42