¹₁₀ of the people at a tourist attraction were men. 80% of the remaining people were women and the rest were children. The total number of men and children is 176 less than the number of women. After some women entered the tourist attraction, 75% of the people that remained were women. How many women entered the tourist attraction?

Men	Children	Women	Total
1x5	9x5		10x5
	1x9	4x9
5	9	36	50

	Men and children	Women
Before	14x1 = 14 u	36x1 = 36 u
Change		+ 6 u
After	1x14 = 14 u	3x14 = 42 u

80% = ⁸⁰₁₀₀ = ⁴₅
Children : Women = 1 : 4

The total number of children and women at first is repeated.  Make the total number of children at first the same. LCM of 9 and 5 is 45.

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 14 and 1 is 14.

The total number of men and children is 176 less than the number of women.

Number of less men and children than the number of women at first
= 36 u - 14 u
= 22 u

22 u = 176

1 u = 176 ÷ 22 = 8

Number of women who entered the tourist attraction
= 42 u - 36 u
= 6 u
= 6 x 8
= 48

Answer(s): 48