¹₁₀ of the people at a concert hall were men. 70% of the remaining people were women and the rest were children. The number of women was 494 more than the total number of men and children. After some women left the concert hall, 50% of the people that remained were women. How many women left the concert hall?

Men	Children	Women	Total
1x10	9x10		10x10
	3x9	7x9
10	27	63	100

	Men and children	Women
Before	37x1 = 37 u	63x1 = 63 u
Change		- 26 u
After	1x37 = 37 u	1x37 = 37 u

70% = ⁷⁰₁₀₀ = ⁷₁₀
Children : Women = 3 : 7

The total number of children and women at first is repeated.  Make the total number of children at first the same. LCM of 9 and 10 is 90.

50% = ⁵⁰₁₀₀ = ¹₂

When some women left, the total number of men and children remains unchanged. Make the total number of men and children the same. LCM of 37 and 1 is 37.

The number of women was 494 more than the total number of men and children at first.

Number of more women than the total number of men and children at first
= 63 u - 37 u
= 26 u

26 u = 494

1 u = 494 ÷ 26 = 19

Number of women who left the concert hall
= 63 u - 37 u
= 26 u
= 26 x 19
= 494

Answer(s): 494