¹₈ of the guests at a stadium were women. 80% of the remaining guests were men and the rest were children. The total number of women and children is 128 less than the number of men. After some men entered the stadium, 75% of the guests that remained were men. How many men entered the stadium?

Women	Children	Men	Total
1x5	7x5		8x5
	1x7	4x7
5	7	28	40

	Women and children	Men
Before	12x1 = 12 u	28x1 = 28 u
Change		+ 8 u
After	1x12 = 12 u	3x12 = 36 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.

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 12 and 1 is 12.

The total number of women and children is 128 less than the number of men.

Number of less women and children than the number of men at first
= 28 u - 12 u
= 16 u

16 u = 128

1 u = 128 ÷ 16 = 8

Number of men who entered the stadium
= 36 u - 28 u
= 8 u
= 8 x 8
= 64

Answer(s): 64