¹₉ of the visitors at a theme park were men. 70% of the remaining visitors were women and the rest were children. The total number of men and children is 198 less than the number of women. After some women entered the theme park, 75% of the visitors that remained were women. How many women entered the theme park?

Men	Children	Women	Total
1x5	8x5		9x5
	3x4	7x4
5	12	28	45

	Men and children	Women
Before	17x1 = 17 u	28x1 = 28 u
Change		+ 23 u
After	1x17 = 17 u	3x17 = 51 u

70% = ⁷⁰₁₀₀ = ⁷₁₀
Children : Women = 3 : 7

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.

75% = ⁷⁵₁₀₀ = ³₄

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 17 and 1 is 17.

The total number of men and children is 198 less than the number of women.

Number of less men and children than the number of women at first
= 28 u - 17 u
= 11 u

11 u = 198

1 u = 198 ÷ 11 = 18

Number of women who entered the theme park
= 51 u - 28 u
= 23 u
= 23 x 18
= 414

Answer(s): 414