At the graduation ceremony, there were 28 less boys than girls. After ¹₂ 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 graduation ceremony at first.

	Boys	Girls	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 boys that remained
= 1 - ¹₂
= ¹₂

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 1 and 3 is 3.

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

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

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

2 u = 28

1 u = 28 ÷ 2 = 14

Number of boys at first
= 6 u
= 6 x 14
= 84

Answer(s): 84