²₉ of the people at a park were men. 70% of the remaining people were women and the rest were children. The number of women was 144 more than the total number of men and children. After some women left the park, 50% of the people that remained were women. How many women left the park?

Men	Children	Women	Total
2x10	7x10		9x10
	3x7	7x7
20	21	49	90

	Men and children	Women
Before	41x1 = 41 u	49x1 = 49 u
Change		- 8 u
After	1x41 = 41 u	1x41 = 41 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 7 and 10 is 70.

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 41 and 1 is 41.

The number of women was 144 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
= 49 u - 41 u
= 8 u

8 u = 144

1 u = 144 ÷ 8 = 18

Number of women who left the park
= 49 u - 41 u
= 8 u
= 8 x 18
= 144

Answer(s): 144