At a conference made up of speakers and participants, there were 10% more women than men. The ratio of the female speakers to male speakers was 3 : 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, 37 female participants left the conference and another 6 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 |
11 groups |
10 groups |
Speakers |
Participants |
Speakers |
Participants |
3 u |
1 p |
1 u |
1 p |
(a)
Number of more women than men
= 100% + 10%
= 110%
110% =
110100 =
1110 Women : Men
11 : 10
3 u + 1 p = 11 groups --- (1)
1 u + 1 p = 10 groups --- (2)
(1) - (2)
11 groups - 10 groups = (3 u + 1 p) - (1 u + 1 p)
1 group = 3 u - 1 u
1 group = 2 u
Number of women
= 11 groups
= 11 x 2 u
= 22 u
Number of female participants
= 22 u - 3 u
= 19 u
Female speakers : Female participants
3 : 19
|
Female Participants |
Male Participants |
Before |
19 u |
19 u |
Change |
- 37 |
+ 6 |
After |
4 boxes |
5 boxes |
4 boxes + 37 = 19 u --- (3)
5 boxes - 6 = 19 u --- (4)
(4) = (3)
5 boxes - 6 = 4 boxes + 37
5 boxes - 4 boxes = 37 + 6
1 box = 43
Number of female participants in the end
= 4 boxes
= 4 x 43
= 172
Number of female participants at first
= 172 + 37
= 209
19 u = 209
1 u = 209 ÷ 19 = 11
Number of speakers
= 3 u + 1 u
= 4 u
= 4 x 11
= 44
Answer(s): (a) 3 : 19; (b) 44