¹₁₀ of the guests at a concert hall were boys. 80% of the remaining guests were girls and the rest were adults. The total number of boys and adults is 132 less than the number of girls. After some girls entered the concert hall, 75% of the guests that remained were girls. How many girls entered the concert hall?

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

	Boys and adults	Girls
Before	14x1 = 14 u	36x1 = 36 u
Change		+ 6 u
After	1x14 = 14 u	3x14 = 42 u

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

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 5 is 45.

75% = ⁷⁵₁₀₀ = ³₄

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

The total number of boys and adults is 132 less than the number of girls.

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

22 u = 132

1 u = 132 ÷ 22 = 6

Number of girls who entered the concert hall
= 42 u - 36 u
= 6 u
= 6 x 6
= 36

Answer(s): 36