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 7 : 3. 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, 16 female participants left the conference and another 8 male participants joined the conference. In the end, there were 56 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 |
7 u |
1 p |
3 u |
1 p |
(a)
Number of more women than men
= 100% + 20%
= 120%
120% =
120100 =
65 Women : Men
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 women
= 6 groups
= 6 x 4 u
= 24 u
Number of female participants
= 24 u - 7 u
= 17 u
Female speakers : Female participants
7 : 17
|
Female Participants |
Male Participants |
Before |
17 u |
17 u |
Change |
- 16 |
+ 8 |
After |
5 boxes |
6 boxes |
5 boxes + 16 = 17 u --- (3)
6 boxes - 8 = 17 u --- (4)
(4) = (3)
6 boxes - 8 = 5 boxes + 16
6 boxes - 5 boxes = 16 + 8
1 box = 24
Number of female participants in the end
= 5 boxes
= 5 x 24
= 120
Number of female participants at first
= 120 + 16
= 136
17 u = 136
1 u = 136 ÷ 17 = 8
Number of speakers
= 7 u + 3 u
= 10 u
= 10 x 8
= 80
Answer(s): (a) 7 : 17; (b) 80