At a conference made up of speakers and participants, there were 25% more women than men. The ratio of the female speakers to male speakers was 9 : 5. 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 34 as many female participants as male participants remaining behind. How many speakers were there at the conference?
Women |
Men |
5 groups |
4 groups |
Speakers |
Participants |
Speakers |
Participants |
9 u |
1 p |
5 u |
1 p |
(a)
Number of more women than men
= 100% + 25%
= 125%
125% =
125100 =
54 Women : Men
5 : 4
9 u + 1 p = 5 groups --- (1)
5 u + 1 p = 4 groups --- (2)
(1) - (2)
5 groups - 4 groups = (9 u + 1 p) - (5 u + 1 p)
1 group = 9 u - 5 u
1 group = 4 u
Number of women
= 5 groups
= 5 x 4 u
= 20 u
Number of female participants
= 20 u - 9 u
= 11 u
Female speakers : Female participants
9 : 11
|
Female Participants |
Male Participants |
Before |
11 u |
11 u |
Change |
- 16 |
+ 8 |
After |
3 boxes |
4 boxes |
3 boxes + 16 = 11 u --- (3)
4 boxes - 8 = 11 u --- (4)
(4) = (3)
4 boxes - 8 = 3 boxes + 16
4 boxes - 3 boxes = 16 + 8
1 box = 24
Number of female participants in the end
= 3 boxes
= 3 x 24
= 72
Number of female participants at first
= 72 + 16
= 88
11 u = 88
1 u = 88 ÷ 11 = 8
Number of speakers
= 9 u + 5 u
= 14 u
= 14 x 8
= 112
Answer(s): (a) 9 : 11; (b) 112