²₉ of the people at a zoo were women. 90% of the remaining people were men and the rest were children. The number of men was 504 more than the total number of women and children. After some men left the zoo, 50% of the people that remained were men. How many men left the zoo?

Women	Children	Men	Total
2x10	7x10		9x10
	1x7	9x7
20	7	63	90

	Women and children	Men
Before	27x1 = 27 u	63x1 = 63 u
Change		- 36 u
After	1x27 = 27 u	1x27 = 27 u

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

The total number of children and men at first is repeated.  Make the total number of children at first the same. LCM of 7 and 10 is 70.

50% = ⁵⁰₁₀₀ = ¹₂

When some men left, the total number of women and children remains unchanged. Make the total number of women and children the same. LCM of 27 and 1 is 27.

The number of men was 504 more than the total number of women and children at first.

Number of more men than the total number of women and children at first
= 63 u - 27 u
= 36 u

36 u = 504

1 u = 504 ÷ 36 = 14

Number of men who left the zoo
= 63 u - 27 u
= 36 u
= 36 x 14
= 504

Answer(s): 504