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 10 : 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, 6 female participants left the conference and another 25 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 |
10 u |
1 p |
3 u |
1 p |
(a)
Number of more women than men
= 100% + 50%
= 150%
150% =
150100 =
32 Women : Men
3 : 2
10 u + 1 p = 3 groups --- (1)
3 u + 1 p = 2 groups --- (2)
(1) - (2)
3 groups - 2 groups = (10 u + 1 p) - (3 u + 1 p)
1 group = 10 u - 3 u
1 group = 7 u
Number of women
= 3 groups
= 3 x 7 u
= 21 u
Number of female participants
= 21 u - 10 u
= 11 u
Female speakers : Female participants
10 : 11
|
Female Participants |
Male Participants |
Before |
11 u |
11 u |
Change |
- 6 |
+ 25 |
After |
3 boxes |
4 boxes |
3 boxes + 6 = 11 u --- (3)
4 boxes - 25 = 11 u --- (4)
(4) = (3)
4 boxes - 25 = 3 boxes + 6
4 boxes - 3 boxes = 6 + 25
1 box = 31
Number of female participants in the end
= 3 boxes
= 3 x 31
= 93
Number of female participants at first
= 93 + 6
= 99
11 u = 99
1 u = 99 ÷ 11 = 9
Number of speakers
= 10 u + 3 u
= 13 u
= 13 x 9
= 117
Answer(s): (a) 10 : 11; (b) 117