¹₉ of the visitors at a museum were women. 80% of the remaining visitors were men and the rest were children. The number of men was 285 more than the total number of women and children. After some men left the museum, 50% of the visitors that remained were men. How many men left the museum?

Women	Children	Men	Total
1x5	8x5		9x5
	1x8	4x8
5	8	32	45

	Women and children	Men
Before	13x1 = 13 u	32x1 = 32 u
Change		- 19 u
After	1x13 = 13 u	1x13 = 13 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 8 and 5 is 40.

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 13 and 1 is 13.

The number of men was 285 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
= 32 u - 13 u
= 19 u

19 u = 285

1 u = 285 ÷ 19 = 15

Number of men who left the museum
= 32 u - 13 u
= 19 u
= 19 x 15
= 285

Answer(s): 285