Australia and France took part in Youth Games. From Australia, the ratio of the number of female supporters to the number of male supporters was 3 : 2. From France, the ratio of the number of female supporters to the number of male supporters was 1 : 5. The total number of supporters from Australia was ⁵₁₂ the total number of supporters from France.

1. What was the ratio of the number of female supporters from Australia to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 132 female supporters from both countries joined the games, the percentage of all the male supporters became 24%. How many less male supporters from Australia than France were there at first?

Australia		France
5 u		12 u
Female supporters	Male supporters	Female supporters	Male supporters
3	2	1x2	5x2
3 u	2 u	2 u	10 u

(a)
Number of female supporters from France
= ¹₆ x 12 u
= 2 u

Number of male supporters from Australia
= ⁵₆ x 12 u
= 10 u

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

Female supporters from Australia : Total female supporters
3 : 5

(b)

	Female supporters	Male supporters
Before	5x2 = 10%	12x2 = 24%
Change	+ 132
After	76%	24%

Number of female supporters in the end in percent
= 100% - 24%
= 76%

Total number of male supporters at first
= 2 u + 10 u
= 12 u

After another 132 female supporters from both countries joined the games, the percentage of all the male supporters became 24%.

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

12 u = 24%

1 u = 24% ÷ 12 = 2%

Number of female supporters at first in percent
= 5 x 2%
= 10%

Number of female supporters from both countries who joined the games
= 76% - 10%
= 66%

66% = 132 

1% = 132 ÷ 66 = 2

Number of less male supporters from Australia than France at first
= 10 u - 2 u
= 8 u
= 8 x 2%
= 16%
= 16 x 2
= 32 

Answer(s): (a) 3 : 5; (b) 32