¹₁₀ of the guests at a bird park were men. 75% of the remaining guests were women and the rest were children. The number of women was 168 more than the total number of men and children. After some women left the bird park, 50% of the guests that remained were women. How many women left the bird park?

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		- 14 u
After	1x13 = 13 u	1x13 = 13 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.

50% = ⁵⁰₁₀₀ = ¹₂

When some women left, 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 number of women was 168 more than the total number of men and children at first.

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

14 u = 168

1 u = 168 ÷ 14 = 12

Number of women who left the bird park
= 27 u - 13 u
= 14 u
= 14 x 12
= 168

Answer(s): 168