At the concert, there were 50 less boys than girls. After ²₅ of the boys and ⁴₉ 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	5x5 = 25 u	9x3 = 27 u	2 u
Change	- 2x5 = - 10 u	- 4x3 = - 12 u
After	3x5 = 15 u	5x3 = 15 u

Fraction of boys that remained
= 1 - ²₅
= ³₅

Fraction of girls that remained
= 1 - ⁴₉
= ⁵₉

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 5 is 15.

^3x5_5x5 Boys = ^5x3_9x3 Girls
¹⁵₂₅ Boys = ¹⁵₂₇ Girls

Total boys at first = 25 u
Total girls at first = 27 u

Number of less boys than girls at first
= 27 u - 25 u
= 2 u

2 u = 50

1 u = 50 ÷ 2 = 25

Number of boys at first
= 25 u
= 25 x 25
= 625

Answer(s): 625