Denmark and Australia took part in Youth Games. From Denmark, the ratio of the number of male supporters to the number of female supporters was 1 : 4. From Australia, the ratio of the number of male supporters to the number of female supporters was 3 : 5. The total number of supporters from Denmark was ⁵₂₄ the total number of supporters from Australia.

1. What was the ratio of the number of male supporters from Denmark to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 378 male supporters from both countries joined the games, the percentage of all the female supporters became 38%. How many less female supporters from Denmark than Australia were there at first?

Denmark		Australia
5 u		24 u
Male supporters	Female supporters	Male supporters	Female supporters
1	4	3x3	5x3
1 u	4 u	9 u	15 u

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

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

Total number of male supporters
= 1 u + 9 u
= 10 u

Male supporters from Denmark : Total male supporters
1 : 10

(b)

	Male supporters	Female supporters
Before	10x2 = 20%	19x2 = 38%
Change	+ 378
After	62%	38%

Number of male supporters in the end in percent
= 100% - 38%
= 62%

Total number of female supporters at first
= 4 u + 15 u
= 19 u

After another 378 male supporters from both countries joined the games, the percentage of all the female supporters became 38%.

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

19 u = 38%

1 u = 38% ÷ 19 = 2%

Number of male supporters at first in percent
= 10 x 2%
= 20%

Number of male supporters from both countries who joined the games
= 62% - 20%
= 42%

42% = 378 

1% = 378 ÷ 42 = 9

Number of less female supporters from Denmark than Australia at first
= 15 u - 4 u
= 11 u
= 11 x 2%
= 22%
= 22 x 9
= 198 

Answer(s): (a) 1 : 10; (b) 198