Australia and Italy took part in Youth Games. From Australia, the ratio of the number of female supporters to the number of male supporters was 3 : 4. From Italy, the ratio of the number of female supporters to the number of male supporters was 2 : 3. The total number of supporters from Australia was ⁷₂₀ the total number of supporters from Italy.

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 56 female supporters from both countries left the games, the percentage of all the male supporters became 64%. How many more male supporters from Italy than Australia were there at first?

Australia		Italy
7 u		20 u
Female supporters	Male supporters	Female supporters	Male supporters
3	4	2x2	3x2
3 u	4 u	8 u	12 u

(a)
Number of female supporters from Italy
= ²₅ x 20 u
= 8 u

Number of male supporters from Australia
= ³₅ x 20 u
= 12 u

Total number of female supporters
= 3 u + 8 u
= 11 u

Female supporters from Australia : Total female supporters
3 : 11

(b)

	Female supporters	Male supporters
Before	11x4 = 44%	16x4 = 64%
Change	- 56
After	36%	64%

Number of female supporters in the end in percent
= 100% - 64%
= 36%

Total number of male supporters at first
= 4 u + 12 u
= 16 u

After 56 female supporters from both countries left the games, the percentage of all the male supporters became 64%.

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

16 u = 64%

1 u = 64% ÷ 16 = 4%

Number of female supporters at first in percent
= 11 x 4%
= 44%

Number of female supporters from both countries who left
= 44% - 36%
= 8%

8% = 56 

1% = 56 ÷ 8 = 7

Number of more male supporters from Italy than Australia at first
= 12 u - 4 u
= 8 u
= 8 x 4%
= 32%
= 32 x 7
= 224 

Answer(s): (a) 3 : 11; (b) 224