¹₁₀ of the people at a museum were boys. 75% of the remaining people were girls and the rest were adults. The total number of boys and adults is 252 less than the number of girls. After some girls entered the museum, 80% of the people that remained were girls. How many girls entered the museum?

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		+ 25 u
After	1x13 = 13 u	4x13 = 52 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.

80% = ⁸⁰₁₀₀ = ⁴₅

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 13 and 1 is 13.

The total number of boys and adults is 252 less than the number of girls.

Number of less boys and adults than the number of girls at first
= 27 u - 13 u
= 14 u

14 u = 252

1 u = 252 ÷ 14 = 18

Number of girls who entered the museum
= 52 u - 27 u
= 25 u
= 25 x 18
= 450

Answer(s): 450