Brunei and Fiji took part in Youth Games. From Brunei, the ratio of the number of female supporters to the number of male supporters was 2 : 9. From Fiji, the ratio of the number of female supporters to the number of male supporters was 1 : 7. The total number of supporters from Brunei was
1124 the total number of supporters from Fiji.
- What was the ratio of the number of female supporters from Brunei to the total number of female supporters from both countries? Express the answer in the simplest form.
- After 30 female supporters from both countries left the games, the percentage of all the male supporters became 90%. How many more male supporters from Fiji than Brunei were there at first?
Brunei |
Fiji |
11 u |
24 u |
Female supporters |
Male supporters |
Female supporters |
Male supporters |
2 |
9 |
1x3 |
7x3 |
2 u |
9 u |
3 u |
21 u |
(a)
Number of female supporters from Fiji
=
18 x 24 u
= 3 u
Number of male supporters from Brunei
=
78 x 24 u
= 21 u
Total number of female supporters
= 2 u + 3 u
= 5 u
Female supporters from Brunei : Total female supporters
2 : 5
(b)
|
Female supporters |
Male supporters |
Before |
5x3 = 15% |
30x3 = 90% |
Change |
- 30 |
|
After |
10% |
90% |
Number of female supporters in the end in percent
= 100% - 90%
= 10%
Total number of male supporters at first
= 9 u + 21 u
= 30 u
After 30 female supporters from both countries left the games, the percentage of all the male supporters became 90%.
Since only female supporters left the games, the number of male supporters remains unchanged. Make the number of male supporters the same.
30 u = 90%
1 u = 90% ÷ 30 =
3%Number of female supporters at first in percent
= 5 x 3%
= 15%
Number of female supporters from both countries who left
= 15% - 10%
= 5%
5% = 30
1% = 30 ÷ 5 =
6Number of more male supporters from Fiji than Brunei at first
= 21 u - 9 u
= 12 u
= 12 x 3%
= 36%
= 36 x 6
= 216
Answer(s): (a) 2 : 5; (b) 216