Australia and Scotland took part in Youth Games. From Australia, the ratio of the number of male supporters to the number of female supporters was 2 : 11. From Scotland, the ratio of the number of male supporters to the number of female supporters was 3 : 5. The total number of supporters from Australia was ¹³₂₄ the total number of supporters from Scotland.

1. What was the ratio of the number of male supporters from Australia to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 260 male supporters from both countries joined the games, the percentage of all the female supporters became 52%. How many less female supporters from Australia than Scotland were there at first?

Australia		Scotland
13 u		24 u
Male supporters	Female supporters	Male supporters	Female supporters
2	11	3x3	5x3
2 u	11 u	9 u	15 u

(a)
Number of male supporters from Scotland
= ³₈ x 24 u
= 9 u

Number of female supporters from Australia
= ⁵₈ x 24 u
= 15 u

Total number of male supporters
= 2 u + 9 u
= 11 u

Male supporters from Australia : Total male supporters
2 : 11

(b)

	Male supporters	Female supporters
Before	11x2 = 22%	26x2 = 52%
Change	+ 260
After	48%	52%

Number of male supporters in the end in percent
= 100% - 52%
= 48%

Total number of female supporters at first
= 11 u + 15 u
= 26 u

After another 260 male supporters from both countries joined the games, the percentage of all the female supporters became 52%.

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

26 u = 52%

1 u = 52% ÷ 26 = 2%

Number of male supporters at first in percent
= 11 x 2%
= 22%

Number of male supporters from both countries who joined the games
= 48% - 22%
= 26%

26% = 260 

1% = 260 ÷ 26 = 10

Number of less female supporters from Australia than Scotland at first
= 15 u - 11 u
= 4 u
= 4 x 2%
= 8%
= 8 x 10
= 80 

Answer(s): (a) 2 : 11; (b) 80