At a conference made up of speakers and participants, there were 50% more men than women. The ratio of the male speakers to female speakers was 8 : 3. There was an equal number of male and female participants.

1. Find the ratio of male speakers to male participants at the conference at first. 
2. Halfway, 8 male participants left the conference and another 15 female participants joined the conference. In the end, there were ³₄ as many male participants as female participants remaining behind. How many speakers were there at the conference?

Men		Women
3 groups		2 groups
Speakers	Participants	Speakers	Participants
8 u	1 p	3 u	1 p

(a)
Number of more men than women
= 100% + 50%
= 150%

150% = ¹⁵⁰₁₀₀ = ³₂

Men : Women
3 : 2

8 u + 1 p = 3 groups --- (1)
3 u + 1 p = 2 groups --- (2)

(1) - (2)
3 groups - 2 groups = (8 u + 1 p) - (3 u + 1 p) 
1 group = 8 u - 3 u
1 group = 5 u

Number of men
= 3 groups
= 3 x 5 u
= 15 u

Number of male participants
= 15 u - 8 u
= 7 u

Male speakers : Male participants
8 : 7 

	Male Participants	Female Participants
Before	7 u	7 u
Change	- 8	+ 15
After	3 boxes	4 boxes

3 boxes + 8 = 7 u --- (3)
4 boxes - 15 = 7 u --- (4)

(4) = (3)
4 boxes - 15 = 3 boxes + 8
4 boxes - 3 boxes = 8 + 15

1 box = 23

Number of male participants in the end
= 3 boxes 
= 3 x 23 
= 69

Number of male participants at first
= 69 + 8 
= 77

7 u = 77

1 u = 77 ÷ 7 = 11

Number of speakers
= 8 u + 3 u
= 11 u
= 11 x 11
= 121

Answer(s): (a) 8 : 7; (b) 121