¹₉ of the guests at a concert hall were boys. 90% of the remaining guests were girls and the rest were adults. The number of girls was 459 more than the total number of boys and adults. After some girls left the concert hall, 75% of the guests that remained were girls. How many girls left the concert hall?

Boys	Adults	Girls	Total
1x5	8x5		9x5
	1x4	9x4
5	4	36	45

	Boys and adults	Girls
Before	9x1 = 9 u	36x1 = 36 u
Change		- 9 u
After	1x9 = 9 u	3x9 = 27 u

90% = ⁹⁰₁₀₀ = ⁹₁₀
Adults : Girls = 1 : 9

The total number of adults and girls at first is repeated.  Make the total number of adults at first the same. LCM of 8 and 10 is 40.

75% = ⁷⁵₁₀₀ = ³₄

When some girls left, the total number of boys and adults remains unchanged. Make the total number of boys and adults the same. LCM of 9 and 1 is 9.

The number of girls was 459 more than the total number of boys and adults at first.

Number of more girls than the total number of boys and adults at first
= 36 u - 9 u
= 27 u

27 u = 459

1 u = 459 ÷ 27 = 17

Number of girls who left the concert hall
= 36 u - 27 u
= 9 u
= 9 x 17
= 153

Answer(s): 153