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 : 1. There was an equal number of male and female participants.
- Find the ratio of male speakers to male participants at the conference at first.
- Halfway, 12 male participants left the conference and another 9 female participants joined the conference. In the end, there were 56 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 |
1 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)
1 u + 1 p = 2 groups --- (2)
(1) - (2)
3 groups - 2 groups = (8 u + 1 p) - (1 u + 1 p)
1 group = 8 u - 1 u
1 group = 7 u
Number of men
= 3 groups
= 3 x 7 u
= 21 u
Number of male participants
= 21 u - 8 u
= 13 u
Male speakers : Male participants
8 : 13
|
Male Participants |
Female Participants |
Before |
13 u |
13 u |
Change |
- 12 |
+ 9 |
After |
5 boxes |
6 boxes |
5 boxes + 12 = 13 u --- (3)
6 boxes - 9 = 13 u --- (4)
(4) = (3)
6 boxes - 9 = 5 boxes + 12
6 boxes - 5 boxes = 12 + 9
1 box = 21
Number of male participants in the end
= 5 boxes
= 5 x 21
= 105
Number of male participants at first
= 105 + 12
= 117
13 u = 117
1 u = 117 ÷ 13 = 9
Number of speakers
= 8 u + 1 u
= 9 u
= 9 x 9
= 81
Answer(s): (a) 8 : 13; (b) 81