At a conference made up of speakers and participants, there were 50% more men than women. The ratio of the male speakers to female speakers was 10 : 3. There was an equal number of male and female participants.
- Find the ratio of male speakers to male participants at the conference at first.
- Halfway, 7 male participants left the conference and another 18 female participants joined the conference. In the end, there were 56 as many male participants as female participants remaining behind. How many speakers were there at the conference?
Men |
Women |
3 groups |
2 groups |
Speakers |
Participants |
Speakers |
Participants |
10 u |
1 p |
3 u |
1 p |
(a)
Number of more men than women
= 100% + 50%
= 150%
150% =
150100 =
32 Men : Women
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 men
= 3 groups
= 3 x 7 u
= 21 u
Number of male participants
= 21 u - 10 u
= 11 u
Male speakers : Male participants
10 : 11
|
Male Participants |
Female Participants |
Before |
11 u |
11 u |
Change |
- 7 |
+ 18 |
After |
5 boxes |
6 boxes |
5 boxes + 7 = 11 u --- (3)
6 boxes - 18 = 11 u --- (4)
(4) = (3)
6 boxes - 18 = 5 boxes + 7
6 boxes - 5 boxes = 7 + 18
1 box = 25
Number of male participants in the end
= 5 boxes
= 5 x 25
= 125
Number of male participants at first
= 125 + 7
= 132
11 u = 132
1 u = 132 ÷ 11 = 12
Number of speakers
= 10 u + 3 u
= 13 u
= 13 x 12
= 156
Answer(s): (a) 10 : 11; (b) 156