At the games fest, there were 78 less girls than boys. After ¹₃ of the girls and ⁴₉ of the boys had left the hall, there was an equal number of girls and boys that remained behind. Find the number of girls who were present at the games fest at first.

	Girls	Boys	Less
Before	3x5 = 15 u	9x2 = 18 u	3 u
Change	- 1x5 = - 5 u	- 4x2 = - 8 u
After	2x5 = 10 u	5x2 = 10 u

Fraction of girls that remained
= 1 - ¹₃
= ²₃

Fraction of boys that remained
= 1 - ⁴₉
= ⁵₉

The number of girls and boys in the end is the same. Make the number of girls and boys in the end the same. LCM  of 2 and 5 is 10.

^2x5_3x5 Girls = ^5x2_9x2 Boys
¹⁰₁₅ Girls = ¹⁰₁₈ Boys

Total girls at first = 15 u
Total boys at first = 18 u

Number of less girls than boys at first
= 18 u - 15 u
= 3 u

3 u = 78

1 u = 78 ÷ 3 = 26

Number of girls at first
= 15 u
= 15 x 26
= 390

Answer(s): 390