Fiji and Korea took part in Youth Games. From Fiji, the ratio of the number of female supporters to the number of male supporters was 2 : 5. From Korea, the ratio of the number of female supporters to the number of male supporters was 1 : 5. The total number of supporters from Fiji was
718 the total number of supporters from Korea.
- What was the ratio of the number of female supporters from Fiji to the total number of female supporters from both countries? Express the answer in the simplest form.
- After another 400 female supporters from both countries joined the games, the percentage of all the male supporters became 40%. How many less male supporters from Fiji than Korea were there at first?
Fiji |
Korea |
7 u |
18 u |
Female supporters |
Male supporters |
Female supporters |
Male supporters |
2 |
5 |
1x3 |
5x3 |
2 u |
5 u |
3 u |
15 u |
(a)
Number of female supporters from Korea
=
16 x 18 u
= 3 u
Number of male supporters from Fiji
=
56 x 18 u
= 15 u
Total number of female supporters
= 2 u + 3 u
= 5 u
Female supporters from Fiji : Total female supporters
2 : 5
(b)
|
Female supporters |
Male supporters |
Before |
5x2 = 10% |
20x2 = 40% |
Change |
+ 400 |
|
After |
60% |
40% |
Number of female supporters in the end in percent
= 100% - 40%
= 60%
Total number of male supporters at first
= 5 u + 15 u
= 20 u
After another 400 female supporters from both countries joined the games, the percentage of all the male supporters became 40%.
Since only more female supporters joined the games, the number of male supporters remains unchanged. Make the number of male supporters the same.
20 u = 40%
1 u = 40% ÷ 20 =
2%Number of female supporters at first in percent
= 5 x 2%
= 10%
Number of female supporters from both countries who joined the games
= 60% - 10%
= 50%
50% = 400
1% = 400 ÷ 50 =
8Number of less male supporters from Fiji than Korea at first
= 15 u - 5 u
= 10 u
= 10 x 2%
= 20%
= 20 x 8
= 160
Answer(s): (a) 2 : 5; (b) 160