¹₁₀ of the people at a concert hall were girls. 80% of the remaining people were boys and the rest were adults. The number of boys was 198 more than the total number of girls and adults. After some boys left the concert hall, 50% of the people that remained were boys. How many boys left the concert hall?

Girls	Adults	Boys	Total
1x5	9x5		10x5
	1x9	4x9
5	9	36	50

	Girls and adults	Boys
Before	14x1 = 14 u	36x1 = 36 u
Change		- 22 u
After	1x14 = 14 u	1x14 = 14 u

80% = ⁸⁰₁₀₀ = ⁴₅
Adults : Boys = 1 : 4

The total number of adults and boys at first is repeated.  Make the total number of adults at first the same. LCM of 9 and 5 is 45.

50% = ⁵⁰₁₀₀ = ¹₂

When some boys left, the total number of girls and adults remains unchanged. Make the total number of girls and adults the same. LCM of 14 and 1 is 14.

The number of boys was 198 more than the total number of girls and adults at first.

Number of more boys than the total number of girls and adults at first
= 36 u - 14 u
= 22 u

22 u = 198

1 u = 198 ÷ 22 = 9

Number of boys who left the concert hall
= 36 u - 14 u
= 22 u
= 22 x 9
= 198

Answer(s): 198