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 : 2. 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 6 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 |
6 groups |
5 groups |
Speakers |
Participants |
Speakers |
Participants |
7 u |
1 p |
2 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)
2 u + 1 p = 5 groups --- (2)
(1) - (2)
6 groups - 5 groups = (7 u + 1 p) - (2 u + 1 p)
1 group = 7 u - 2 u
1 group = 5 u
Number of men
= 6 groups
= 6 x 5 u
= 30 u
Number of male participants
= 30 u - 7 u
= 23 u
Male speakers : Male participants
7 : 23
|
Male Participants |
Female Participants |
Before |
23 u |
23 u |
Change |
- 18 |
+ 6 |
After |
5 boxes |
6 boxes |
5 boxes + 18 = 23 u --- (3)
6 boxes - 6 = 23 u --- (4)
(4) = (3)
6 boxes - 6 = 5 boxes + 18
6 boxes - 5 boxes = 18 + 6
1 box = 24
Number of male participants in the end
= 5 boxes
= 5 x 24
= 120
Number of male participants at first
= 120 + 18
= 138
23 u = 138
1 u = 138 ÷ 23 = 6
Number of speakers
= 7 u + 2 u
= 9 u
= 9 x 6
= 54
Answer(s): (a) 7 : 23; (b) 54