Chile and Australia took part in Youth Games. From Chile, the ratio of the number of female supporters to the number of male supporters was 3 : 8. From Australia, the ratio of the number of female supporters to the number of male supporters was 1 : 11. The total number of supporters from Chile was ¹¹₂₄ the total number of supporters from Australia.

1. What was the ratio of the number of female supporters from Chile to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After 15 female supporters from both countries left the games, the percentage of all the male supporters became 90%. How many more male supporters from Australia than Chile were there at first?

Chile		Australia
11 u		24 u
Female supporters	Male supporters	Female supporters	Male supporters
3	8	1x2	11x2
3 u	8 u	2 u	22 u

(a)
Number of female supporters from Australia
= ¹₁₂ x 24 u
= 2 u

Number of male supporters from Chile
= ¹¹₁₂ x 24 u
= 22 u

Total number of female supporters
= 3 u + 2 u
= 5 u

Female supporters from Chile : Total female supporters
3 : 5

(b)

	Female supporters	Male supporters
Before	5x3 = 15%	30x3 = 90%
Change	- 15
After	10%	90%

Number of female supporters in the end in percent
= 100% - 90%
= 10%

Total number of male supporters at first
= 8 u + 22 u
= 30 u

After 15 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% = 15 

1% = 15 ÷ 5 = 3

Number of more male supporters from Australia than Chile at first
= 22 u - 8 u
= 14 u
= 14 x 3%
= 42%
= 42 x 3
= 126 

Answer(s): (a) 3 : 5; (b) 126