Norway and Korea took part in Youth Games. From Norway, the ratio of the number of male supporters to the number of female supporters was 1 : 10. From Korea, the ratio of the number of male supporters to the number of female supporters was 1 : 5. The total number of supporters from Norway was
1118 the total number of supporters from Korea.
- What was the ratio of the number of male supporters from Norway to the total number of male supporters from both countries? Express the answer in the simplest form.
- After another 156 male supporters from both countries joined the games, the percentage of all the female supporters became 75%. How many less female supporters from Norway than Korea were there at first?
Norway |
Korea |
11 u |
18 u |
Male supporters |
Female supporters |
Male supporters |
Female supporters |
1 |
10 |
1x3 |
5x3 |
1 u |
10 u |
3 u |
15 u |
(a)
Number of male supporters from Korea
=
16 x 18 u
= 3 u
Number of female supporters from Norway
=
56 x 18 u
= 15 u
Total number of male supporters
= 1 u + 3 u
= 4 u
Male supporters from Norway : Total male supporters
1 : 4
(b)
|
Male supporters |
Female supporters |
Before |
4x3 = 12% |
25x3 = 75% |
Change |
+ 156 |
|
After |
25% |
75% |
Number of male supporters in the end in percent
= 100% - 75%
= 25%
Total number of female supporters at first
= 10 u + 15 u
= 25 u
After another 156 male supporters from both countries joined the games, the percentage of all the female supporters became 75%.
Since only more male supporters joined the games, the number of female supporters remains unchanged. Make the number of female supporters the same.
25 u = 75%
1 u = 75% ÷ 25 =
3%Number of male supporters at first in percent
= 4 x 3%
= 12%
Number of male supporters from both countries who joined the games
= 25% - 12%
= 13%
13% = 156
1% = 156 ÷ 13 =
12Number of less female supporters from Norway than Korea at first
= 15 u - 10 u
= 5 u
= 5 x 3%
= 15%
= 15 x 12
= 180
Answer(s): (a) 1 : 4; (b) 180