At a conference made up of speakers and participants, there were 10% more men than women. The ratio of the male speakers to female speakers was 3 : 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, 17 male participants left the conference and another 9 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 |
11 groups |
10 groups |
Speakers |
Participants |
Speakers |
Participants |
3 u |
1 p |
1 u |
1 p |
(a)
Number of more men than women
= 100% + 10%
= 110%
110% =
110100 =
1110 Men : Women
11 : 10
3 u + 1 p = 11 groups --- (1)
1 u + 1 p = 10 groups --- (2)
(1) - (2)
11 groups - 10 groups = (3 u + 1 p) - (1 u + 1 p)
1 group = 3 u - 1 u
1 group = 2 u
Number of men
= 11 groups
= 11 x 2 u
= 22 u
Number of male participants
= 22 u - 3 u
= 19 u
Male speakers : Male participants
3 : 19
|
Male Participants |
Female Participants |
Before |
19 u |
19 u |
Change |
- 17 |
+ 9 |
After |
3 boxes |
4 boxes |
3 boxes + 17 = 19 u --- (3)
4 boxes - 9 = 19 u --- (4)
(4) = (3)
4 boxes - 9 = 3 boxes + 17
4 boxes - 3 boxes = 17 + 9
1 box = 26
Number of male participants in the end
= 3 boxes
= 3 x 26
= 78
Number of male participants at first
= 78 + 17
= 95
19 u = 95
1 u = 95 ÷ 19 = 5
Number of speakers
= 3 u + 1 u
= 4 u
= 4 x 5
= 20
Answer(s): (a) 3 : 19; (b) 20