Finland and Kenya took part in Youth Games. From Finland, the ratio of the number of female supporters to the number of male supporters was 4 : 3. From Kenya, the ratio of the number of female supporters to the number of male supporters was 3 : 5. The total number of supporters from Finland was
724 the total number of supporters from Kenya.
- What was the ratio of the number of female supporters from Finland to the total number of female supporters from both countries? Express the answer in the simplest form.
- After another 49 female supporters from both countries joined the games, the percentage of all the male supporters became 54%. How many less male supporters from Finland than Kenya were there at first?
Finland |
Kenya |
7 u |
24 u |
Female supporters |
Male supporters |
Female supporters |
Male supporters |
4 |
3 |
3x3 |
5x3 |
4 u |
3 u |
9 u |
15 u |
(a)
Number of female supporters from Kenya
=
38 x 24 u
= 9 u
Number of male supporters from Finland
=
58 x 24 u
= 15 u
Total number of female supporters
= 4 u + 9 u
= 13 u
Female supporters from Finland : Total female supporters
4 : 13
(b)
|
Female supporters |
Male supporters |
Before |
13x3 = 39% |
18x3 = 54% |
Change |
+ 49 |
|
After |
46% |
54% |
Number of female supporters in the end in percent
= 100% - 54%
= 46%
Total number of male supporters at first
= 3 u + 15 u
= 18 u
After another 49 female supporters from both countries joined the games, the percentage of all the male supporters became 54%.
Since only more female supporters joined the games, the number of male supporters remains unchanged. Make the number of male supporters the same.
18 u = 54%
1 u = 54% ÷ 18 =
3%Number of female supporters at first in percent
= 13 x 3%
= 39%
Number of female supporters from both countries who joined the games
= 46% - 39%
= 7%
7% = 49
1% = 49 ÷ 7 =
7Number of less male supporters from Finland than Kenya at first
= 15 u - 3 u
= 12 u
= 12 x 3%
= 36%
= 36 x 7
= 252
Answer(s): (a) 4 : 13; (b) 252