¹₁₀ of the guests at a concert hall were boys. 75% of the remaining guests were girls and the rest were adults. The number of girls was 224 more than the total number of boys and adults. After some girls left the concert hall, 50% of the guests that remained were girls. How many girls left the concert hall?

Boys	Adults	Girls	Total
1x4	9x4		10x4
	1x9	3x9
4	9	27	40

	Boys and adults	Girls
Before	13x1 = 13 u	27x1 = 27 u
Change		- 14 u
After	1x13 = 13 u	1x13 = 13 u

75% = ⁷⁵₁₀₀ = ³₄
Adults : Girls = 1 : 3

The total number of adults and girls at first is repeated.  Make the total number of adults at first the same. LCM of 9 and 4 is 36.

50% = ⁵⁰₁₀₀ = ¹₂

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 13 and 1 is 13.

The number of girls was 224 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
= 27 u - 13 u
= 14 u

14 u = 224

1 u = 224 ÷ 14 = 16

Number of girls who left the concert hall
= 27 u - 13 u
= 14 u
= 14 x 16
= 224

Answer(s): 224