²₉ of the people at a stadium were boys. 90% of the remaining people were girls and the rest were adults. The total number of boys and adults is 576 less than the number of girls. After some girls entered the stadium, 75% of the people that remained were girls. How many girls entered the stadium?

Boys	Adults	Girls	Total
2x10	7x10		9x10
	1x7	9x7
20	7	63	90

	Boys and adults	Girls
Before	27x1 = 27 u	63x1 = 63 u
Change		+ 18 u
After	1x27 = 27 u	3x27 = 81 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 7 and 10 is 70.

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 27 and 1 is 27.

The total number of boys and adults is 576 less than the number of girls.

Number of less boys and adults than the number of girls at first
= 63 u - 27 u
= 36 u

36 u = 576

1 u = 576 ÷ 36 = 16

Number of girls who entered the stadium
= 81 u - 63 u
= 18 u
= 18 x 16
= 288

Answer(s): 288