At a conference made up of speakers and participants, there were 50% more women than men. The ratio of the female speakers to male speakers was 8 : 1. 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, 23 female participants left the conference and another 7 male participants joined the conference. In the end, there were 45 as many female participants as male participants remaining behind. How many speakers were there at the conference?
Women |
Men |
3 groups |
2 groups |
Speakers |
Participants |
Speakers |
Participants |
8 u |
1 p |
1 u |
1 p |
(a)
Number of more women than men
= 100% + 50%
= 150%
150% =
150100 =
32 Women : Men
3 : 2
8 u + 1 p = 3 groups --- (1)
1 u + 1 p = 2 groups --- (2)
(1) - (2)
3 groups - 2 groups = (8 u + 1 p) - (1 u + 1 p)
1 group = 8 u - 1 u
1 group = 7 u
Number of women
= 3 groups
= 3 x 7 u
= 21 u
Number of female participants
= 21 u - 8 u
= 13 u
Female speakers : Female participants
8 : 13
|
Female Participants |
Male Participants |
Before |
13 u |
13 u |
Change |
- 23 |
+ 7 |
After |
4 boxes |
5 boxes |
4 boxes + 23 = 13 u --- (3)
5 boxes - 7 = 13 u --- (4)
(4) = (3)
5 boxes - 7 = 4 boxes + 23
5 boxes - 4 boxes = 23 + 7
1 box = 30
Number of female participants in the end
= 4 boxes
= 4 x 30
= 120
Number of female participants at first
= 120 + 23
= 143
13 u = 143
1 u = 143 ÷ 13 = 11
Number of speakers
= 8 u + 1 u
= 9 u
= 9 x 11
= 99
Answer(s): (a) 8 : 13; (b) 99