¹₁₀ of the guests at a stadium were men. 75% of the remaining guests were women and the rest were children. The total number of men and children is 266 less than the number of women. After some women entered the stadium, 75% of the guests that remained were women. How many women entered the stadium?

Men	Children	Women	Total
1x4	9x4		10x4
	1x9	3x9
4	9	27	40

	Men and children	Women
Before	13x1 = 13 u	27x1 = 27 u
Change		+ 12 u
After	1x13 = 13 u	3x13 = 39 u

75% = ⁷⁵₁₀₀ = ³₄
Children : Women = 1 : 3

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 4 is 36.

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 13 and 1 is 13.

The total number of men and children is 266 less than the number of women.

Number of less men and children than the number of women at first
= 27 u - 13 u
= 14 u

14 u = 266

1 u = 266 ÷ 14 = 19

Number of women who entered the stadium
= 39 u - 27 u
= 12 u
= 12 x 19
= 228

Answer(s): 228