At the concert, there were 35 less boys than girls. After ¹₃ of the boys and ⁵₈ 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 concert at first.

	Boys	Girls	Less
Before	3x3 = 9 u	8x2 = 16 u	7 u
Change	- 1x3 = - 3 u	- 5x2 = - 10 u
After	2x3 = 6 u	3x2 = 6 u

Fraction of boys that remained
= 1 - ¹₃
= ²₃

Fraction of girls that remained
= 1 - ⁵₈
= ³₈

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 3 is 6.

^2x3_3x3 Boys = ^3x2_8x2 Girls
⁶₉ Boys = ⁶₁₆ Girls

Total boys at first = 9 u
Total girls at first = 16 u

Number of less boys than girls at first
= 16 u - 9 u
= 7 u

7 u = 35

1 u = 35 ÷ 7 = 5

Number of boys at first
= 9 u
= 9 x 5
= 45

Answer(s): 45