¹₁₀ of the people at a park were women. 70% of the remaining people were men and the rest were children. The number of men was 416 more than the total number of women and children. After some men left the park, 50% of the people that remained were men. How many men left the park?

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

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

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

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

The number of men was 416 more than the total number of women and children at first.

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

26 u = 416

1 u = 416 ÷ 26 = 16

Number of men who left the park
= 63 u - 37 u
= 26 u
= 26 x 16
= 416

Answer(s): 416