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

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

	Men and children	Women
Before	12x1 = 12 u	28x1 = 28 u
Change		+ 20 u
After	1x12 = 12 u	4x12 = 48 u

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

The total number of children and women 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 women entered, the total number of men and children remains unchanged. Make the total number of men and children the same. LCM of 12 and 1 is 12.

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

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

16 u = 128

1 u = 128 ÷ 16 = 8

Number of women who entered the concert hall
= 48 u - 28 u
= 20 u
= 20 x 8
= 160

Answer(s): 160