¹₉ of the visitors at a park were men. 90% of the remaining visitors were women and the rest were children. The total number of men and children is 324 less than the number of women. After some women entered the park, 90% of the visitors that remained were women. How many women entered the park?

Men	Children	Women	Total
1x5	8x5		9x5
	1x4	9x4
5	4	36	45

	Men and children	Women
Before	9x1 = 9 u	36x1 = 36 u
Change		+ 45 u
After	1x9 = 9 u	9x9 = 81 u

90% = ⁹⁰₁₀₀ = ⁹₁₀
Children : Women = 1 : 9

The total number of children and women at first is repeated.  Make the total number of children at first the same. LCM of 8 and 10 is 40.

90% = ⁹⁰₁₀₀ = ⁹₁₀

When some women entered, the total number of men and children remains unchanged. Make the total number of men and children the same. LCM of 9 and 1 is 9.

The total number of men and children is 324 less than the number of women.

Number of less men and children than the number of women at first
= 36 u - 9 u
= 27 u

27 u = 324

1 u = 324 ÷ 27 = 12

Number of women who entered the park
= 81 u - 36 u
= 45 u
= 45 x 12
= 540

Answer(s): 540