Australia and Iran took part in Youth Games. From Australia, the ratio of the number of male supporters to the number of female supporters was 3 : 4. From Iran, the ratio of the number of male supporters to the number of female supporters was 1 : 5. The total number of supporters from Australia was ⁷₂₄ the total number of supporters from Iran.

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 28 male supporters from both countries joined the games, the percentage of all the female supporters became 72%. How many less female supporters from Australia than Iran were there at first?

Australia		Iran
7 u		24 u
Male supporters	Female supporters	Male supporters	Female supporters
3	4	1x2	5x2
3 u	4 u	4 u	20 u

(a)
Number of male supporters from Iran
= ¹₆ x 24 u
= 4 u

Number of female supporters from Australia
= ⁵₆ x 24 u
= 20 u

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

Male supporters from Australia : Total male supporters
3 : 7

(b)

	Male supporters	Female supporters
Before	7x3 = 21%	24x3 = 72%
Change	+ 28
After	28%	72%

Number of male supporters in the end in percent
= 100% - 72%
= 28%

Total number of female supporters at first
= 4 u + 20 u
= 24 u

After another 28 male supporters from both countries joined the games, the percentage of all the female supporters became 72%.

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

24 u = 72%

1 u = 72% ÷ 24 = 3%

Number of male supporters at first in percent
= 7 x 3%
= 21%

Number of male supporters from both countries who joined the games
= 28% - 21%
= 7%

7% = 28 

1% = 28 ÷ 7 = 4

Number of less female supporters from Australia than Iran at first
= 20 u - 4 u
= 16 u
= 16 x 3%
= 48%
= 48 x 4
= 192 

Answer(s): (a) 3 : 7; (b) 192