¹₉ of the visitors at a museum were boys. 90% of the remaining visitors were girls and the rest were adults. The total number of boys and adults is 513 less than the number of girls. After some girls entered the museum, 90% of the visitors that remained were girls. How many girls entered the museum?

Boys	Adults	Girls	Total
1x5	8x5		9x5
	1x4	9x4
5	4	36	45

	Boys and adults	Girls
Before	9x1 = 9 u	36x1 = 36 u
Change		+ 45 u
After	1x9 = 9 u	9x9 = 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 8 and 10 is 40.

90% = ⁹⁰₁₀₀ = ⁹₁₀

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 9 and 1 is 9.

The total number of boys and adults is 513 less than the number of girls.

Number of less boys and adults than the number of girls at first
= 36 u - 9 u
= 27 u

27 u = 513

1 u = 513 ÷ 27 = 19

Number of girls who entered the museum
= 81 u - 36 u
= 45 u
= 45 x 19
= 855

Answer(s): 855