At the musical performance, there were 45 less girls than boys. After ³₅ of the girls and ⁶₇ 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 musical performance at first.

	Girls	Boys	Less
Before	5x1 = 5 u	7x2 = 14 u	9 u
Change	- 3x1 = - 3 u	- 6x2 = - 12 u
After	2x1 = 2 u	1x2 = 2 u

Fraction of girls that remained
= 1 - ³₅
= ²₅

Fraction of boys that remained
= 1 - ⁶₇
= ¹₇

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 1 is 2.

^2x1_5x1 Girls = ^1x2_7x2 Boys
²₅ Girls = ²₁₄ Boys

Total girls at first = 5 u
Total boys at first = 14 u

Number of less girls than boys at first
= 14 u - 5 u
= 9 u

9 u = 45

1 u = 45 ÷ 9 = 5

Number of girls at first
= 5 u
= 5 x 5
= 25

Answer(s): 25