At a conference made up of speakers and participants, there were 25% more men than women. The ratio of the male speakers to female speakers was 9 : 5. 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, 24 male participants left the conference and another 3 female participants joined the conference. In the end, there were 45 as many male participants as female participants remaining behind. How many speakers were there at the conference?
Men |
Women |
5 groups |
4 groups |
Speakers |
Participants |
Speakers |
Participants |
9 u |
1 p |
5 u |
1 p |
(a)
Number of more men than women
= 100% + 25%
= 125%
125% =
125100 =
54 Men : Women
5 : 4
9 u + 1 p = 5 groups --- (1)
5 u + 1 p = 4 groups --- (2)
(1) - (2)
5 groups - 4 groups = (9 u + 1 p) - (5 u + 1 p)
1 group = 9 u - 5 u
1 group = 4 u
Number of men
= 5 groups
= 5 x 4 u
= 20 u
Number of male participants
= 20 u - 9 u
= 11 u
Male speakers : Male participants
9 : 11
|
Male Participants |
Female Participants |
Before |
11 u |
11 u |
Change |
- 24 |
+ 3 |
After |
4 boxes |
5 boxes |
4 boxes + 24 = 11 u --- (3)
5 boxes - 3 = 11 u --- (4)
(4) = (3)
5 boxes - 3 = 4 boxes + 24
5 boxes - 4 boxes = 24 + 3
1 box = 27
Number of male participants in the end
= 4 boxes
= 4 x 27
= 108
Number of male participants at first
= 108 + 24
= 132
11 u = 132
1 u = 132 ÷ 11 = 12
Number of speakers
= 9 u + 5 u
= 14 u
= 14 x 12
= 168
Answer(s): (a) 9 : 11; (b) 168