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, 32 female participants left the conference and another 5 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 |
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 |
- 32 |
+ 5 |
After |
3 boxes |
4 boxes |
3 boxes + 32 = 13 u --- (3)
4 boxes - 5 = 13 u --- (4)
(4) = (3)
4 boxes - 5 = 3 boxes + 32
4 boxes - 3 boxes = 32 + 5
1 box = 37
Number of female participants in the end
= 3 boxes
= 3 x 37
= 111
Number of female participants at first
= 111 + 32
= 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