²₉ of the guests at a zoo were women. 80% of the remaining guests were men and the rest were children. The number of men was 176 more than the total number of women and children. After some men left the zoo, 50% of the guests that remained were men. How many men left the zoo?

Women	Children	Men	Total
2x5	7x5		9x5
	1x7	4x7
10	7	28	45

	Women and children	Men
Before	17x1 = 17 u	28x1 = 28 u
Change		- 11 u
After	1x17 = 17 u	1x17 = 17 u

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

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 5 is 35.

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 17 and 1 is 17.

The number of men was 176 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
= 28 u - 17 u
= 11 u

11 u = 176

1 u = 176 ÷ 11 = 16

Number of men who left the zoo
= 28 u - 17 u
= 11 u
= 11 x 16
= 176

Answer(s): 176