²₉ of the visitors at a zoo were women. 80% of the remaining visitors were men and the rest were children. The total number of women and children is 176 less than the number of men. After some men entered the zoo, 80% of the visitors that remained were men. How many men entered 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		+ 40 u
After	1x17 = 17 u	4x17 = 68 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.

80% = ⁸⁰₁₀₀ = ⁴₅

When some men entered, 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 total number of women and children is 176 less than the number of men.

Number of less women and children than the number of men at first
= 28 u - 17 u
= 11 u

11 u = 176

1 u = 176 ÷ 11 = 16

Number of men who entered the zoo
= 68 u - 28 u
= 40 u
= 40 x 16
= 640

Answer(s): 640