At a conference made up of speakers and participants, there were 20% more women than men. The ratio of the female speakers to male speakers was 5 : 2. There was an equal number of female and male participants.
- Find the ratio of female speakers to female participants at the conference at first.
- Halfway, 20 female participants left the conference and another 8 male participants joined the conference. In the end, there were 34 as many female participants as male participants remaining behind. How many speakers were there at the conference?
Women |
Men |
6 groups |
5 groups |
Speakers |
Participants |
Speakers |
Participants |
5 u |
1 p |
2 u |
1 p |
(a)
Number of more women than men
= 100% + 20%
= 120%
120% =
120100 =
65 Women : Men
6 : 5
5 u + 1 p = 6 groups --- (1)
2 u + 1 p = 5 groups --- (2)
(1) - (2)
6 groups - 5 groups = (5 u + 1 p) - (2 u + 1 p)
1 group = 5 u - 2 u
1 group = 3 u
Number of women
= 6 groups
= 6 x 3 u
= 18 u
Number of female participants
= 18 u - 5 u
= 13 u
Female speakers : Female participants
5 : 13
|
Female Participants |
Male Participants |
Before |
13 u |
13 u |
Change |
- 20 |
+ 8 |
After |
3 boxes |
4 boxes |
3 boxes + 20 = 13 u --- (3)
4 boxes - 8 = 13 u --- (4)
(4) = (3)
4 boxes - 8 = 3 boxes + 20
4 boxes - 3 boxes = 20 + 8
1 box = 28
Number of female participants in the end
= 3 boxes
= 3 x 28
= 84
Number of female participants at first
= 84 + 20
= 104
13 u = 104
1 u = 104 ÷ 13 = 8
Number of speakers
= 5 u + 2 u
= 7 u
= 7 x 8
= 56
Answer(s): (a) 5 : 13; (b) 56