Denmark and Japan took part in Youth Games. From Denmark, the ratio of the number of female supporters to the number of male supporters was 3 : 4. From Japan, the ratio of the number of female supporters to the number of male supporters was 2 : 9. The total number of supporters from Denmark was ⁷₂₂ the total number of supporters from Japan.

1. What was the ratio of the number of female supporters from Denmark to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After 96 female supporters from both countries left the games, the percentage of all the male supporters became 88%. How many more male supporters from Japan than Denmark were there at first?

Denmark		Japan
7 u		22 u
Female supporters	Male supporters	Female supporters	Male supporters
3	4	2x2	9x2
3 u	4 u	4 u	18 u

(a)
Number of female supporters from Japan
= ²₁₁ x 22 u
= 4 u

Number of male supporters from Denmark
= ⁹₁₁ x 22 u
= 18 u

Total number of female supporters
= 3 u + 4 u
= 7 u

Female supporters from Denmark : Total female supporters
3 : 7

(b)

	Female supporters	Male supporters
Before	7x4 = 28%	22x4 = 88%
Change	- 96
After	12%	88%

Number of female supporters in the end in percent
= 100% - 88%
= 12%

Total number of male supporters at first
= 4 u + 18 u
= 22 u

After 96 female supporters from both countries left the games, the percentage of all the male supporters became 88%.

Since only female supporters left the games, the number of male supporters remains unchanged. Make the number of male supporters the same.

22 u = 88%

1 u = 88% ÷ 22 = 4%

Number of female supporters at first in percent
= 7 x 4%
= 28%

Number of female supporters from both countries who left
= 28% - 12%
= 16%

16% = 96 

1% = 96 ÷ 16 = 6

Number of more male supporters from Japan than Denmark at first
= 18 u - 4 u
= 14 u
= 14 x 4%
= 56%
= 56 x 6
= 336 

Answer(s): (a) 3 : 7; (b) 336