At a conference made up of speakers and participants, there were 20% more men than women. The ratio of the male speakers to female speakers was 7 : 3. 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, 21 male participants left the conference and another 6 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 |
6 groups |
5 groups |
Speakers |
Participants |
Speakers |
Participants |
7 u |
1 p |
3 u |
1 p |
(a)
Number of more men than women
= 100% + 20%
= 120%
120% =
120100 =
65 Men : Women
6 : 5
7 u + 1 p = 6 groups --- (1)
3 u + 1 p = 5 groups --- (2)
(1) - (2)
6 groups - 5 groups = (7 u + 1 p) - (3 u + 1 p)
1 group = 7 u - 3 u
1 group = 4 u
Number of men
= 6 groups
= 6 x 4 u
= 24 u
Number of male participants
= 24 u - 7 u
= 17 u
Male speakers : Male participants
7 : 17
|
Male Participants |
Female Participants |
Before |
17 u |
17 u |
Change |
- 21 |
+ 6 |
After |
3 boxes |
4 boxes |
3 boxes + 21 = 17 u --- (3)
4 boxes - 6 = 17 u --- (4)
(4) = (3)
4 boxes - 6 = 3 boxes + 21
4 boxes - 3 boxes = 21 + 6
1 box = 27
Number of male participants in the end
= 3 boxes
= 3 x 27
= 81
Number of male participants at first
= 81 + 21
= 102
17 u = 102
1 u = 102 ÷ 17 = 6
Number of speakers
= 7 u + 3 u
= 10 u
= 10 x 6
= 60
Answer(s): (a) 7 : 17; (b) 60