¹₈ of the guests at a zoo were women. 75% of the remaining guests were men and the rest were children. The total number of women and children is 140 less than the number of men. After some men entered the zoo, 75% of the guests that remained were men. How many men entered the zoo?

Women	Children	Men	Total
1x4	7x4		8x4
	1x7	3x7
4	7	21	32

	Women and children	Men
Before	11x1 = 11 u	21x1 = 21 u
Change		+ 12 u
After	1x11 = 11 u	3x11 = 33 u

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

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 4 is 28.

75% = ⁷⁵₁₀₀ = ³₄

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 11 and 1 is 11.

The total number of women and children is 140 less than the number of men.

Number of less women and children than the number of men at first
= 21 u - 11 u
= 10 u

10 u = 140

1 u = 140 ÷ 10 = 14

Number of men who entered the zoo
= 33 u - 21 u
= 12 u
= 12 x 14
= 168

Answer(s): 168