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 5 : 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, 18 male participants left the conference and another 4 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 |
5 u |
1 p |
3 u |
1 p |
(a)
Number of more men than women
= 100% + 20%
= 120%
120% =
120100 =
65 Men : Women
6 : 5
5 u + 1 p = 6 groups --- (1)
3 u + 1 p = 5 groups --- (2)
(1) - (2)
6 groups - 5 groups = (5 u + 1 p) - (3 u + 1 p)
1 group = 5 u - 3 u
1 group = 2 u
Number of men
= 6 groups
= 6 x 2 u
= 12 u
Number of male participants
= 12 u - 5 u
= 7 u
Male speakers : Male participants
5 : 7
|
Male Participants |
Female Participants |
Before |
7 u |
7 u |
Change |
- 18 |
+ 4 |
After |
3 boxes |
4 boxes |
3 boxes + 18 = 7 u --- (3)
4 boxes - 4 = 7 u --- (4)
(4) = (3)
4 boxes - 4 = 3 boxes + 18
4 boxes - 3 boxes = 18 + 4
1 box = 22
Number of male participants in the end
= 3 boxes
= 3 x 22
= 66
Number of male participants at first
= 66 + 18
= 84
7 u = 84
1 u = 84 ÷ 7 = 12
Number of speakers
= 5 u + 3 u
= 8 u
= 8 x 12
= 96
Answer(s): (a) 5 : 7; (b) 96