¹₉ of the people at a park were women. 80% of the remaining people were men and the rest were children. The total number of women and children is 323 less than the number of men. After some men entered the park, 75% of the people that remained were men. How many men entered the park?

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		+ 7 u
After	1x13 = 13 u	3x13 = 39 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.

75% = ⁷⁵₁₀₀ = ³₄

When some men entered, 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 total number of women and children is 323 less than the number of men.

Number of less women and children than the number of men at first
= 32 u - 13 u
= 19 u

19 u = 323

1 u = 323 ÷ 19 = 17

Number of men who entered the park
= 39 u - 32 u
= 7 u
= 7 x 17
= 119

Answer(s): 119