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 7 : 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, 21 female participants left the conference and another 6 male participants joined the conference. In the end, there were 56 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 |
7 u |
1 p |
3 u |
1 p |
(a)
Number of more women than men
= 100% + 25%
= 125%
125% =
125100 =
54 Women : Men
5 : 4
7 u + 1 p = 5 groups --- (1)
3 u + 1 p = 4 groups --- (2)
(1) - (2)
5 groups - 4 groups = (7 u + 1 p) - (3 u + 1 p)
1 group = 7 u - 3 u
1 group = 4 u
Number of women
= 5 groups
= 5 x 4 u
= 20 u
Number of female participants
= 20 u - 7 u
= 13 u
Female speakers : Female participants
7 : 13
|
Female Participants |
Male Participants |
Before |
13 u |
13 u |
Change |
- 21 |
+ 6 |
After |
5 boxes |
6 boxes |
5 boxes + 21 = 13 u --- (3)
6 boxes - 6 = 13 u --- (4)
(4) = (3)
6 boxes - 6 = 5 boxes + 21
6 boxes - 5 boxes = 21 + 6
1 box = 27
Number of female participants in the end
= 5 boxes
= 5 x 27
= 135
Number of female participants at first
= 135 + 21
= 156
13 u = 156
1 u = 156 ÷ 13 = 12
Number of speakers
= 7 u + 3 u
= 10 u
= 10 x 12
= 120
Answer(s): (a) 7 : 13; (b) 120