At a dinner function, ⁴₇ of the guests were men and the rest were women. Some men then left the dinner function and the remaining number of men were ³₈ of the guests. 69 men then joined the dinner function. The number of guests in the end was 36 more than the number of guests at first. How many guests were there at first?

	Men	Women	Total
Before	4x5 = 20 u	3x5 = 15 u	7x5 = 35 u
Change 1	- ?
After 1	3x3 = 9 u	5x3 = 15 u
Change 2	+ 69
After 2	9 u + 69	15 u	24 u + 69

The number of women remains unchanged.  Make the number of women the same.  LCM of 3 and 5 is 15.

The number of guests in the end was 36 more than the number of guests at first.
If 36 guests are added to the number of guests at first, the number of guests in the end and at first will be the same.

35 u + 36 = 24 u + 69
35 u - 24 u = 69 - 36
11 u = 33

1 u = 33 ÷ 11 = 3

Number of guests at first
= 35 u
= 35 x 3
= 105

Answer(s): 105