At the graduation ceremony, there were 52 less boys than girls. After ²₅ of the boys and ⁵₆ 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	5x1 = 5 u	6x3 = 18 u	13 u
Change	- 2x1 = - 2 u	- 5x3 = - 15 u
After	3x1 = 3 u	1x3 = 3 u

Fraction of boys that remained
= 1 - ²₅
= ³₅

Fraction of girls that remained
= 1 - ⁵₆
= ¹₆

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 3 and 1 is 3.

^3x1_5x1 Boys = ^1x3_6x3 Girls
³₅ Boys = ³₁₈ Girls

Total boys at first = 5 u
Total girls at first = 18 u

Number of less boys than girls at first
= 18 u - 5 u
= 13 u

13 u = 52

1 u = 52 ÷ 13 = 4

Number of boys at first
= 5 u
= 5 x 4
= 20

Answer(s): 20