Sweden and Korea took part in Youth Games. From Sweden, the ratio of the number of female supporters to the number of male supporters was 1 : 6. From Korea, the ratio of the number of female supporters to the number of male supporters was 1 : 5. The total number of supporters from Sweden was ⁷₁₈ the total number of supporters from Korea.

1. What was the ratio of the number of female supporters from Sweden to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 250 female supporters from both countries joined the games, the percentage of all the male supporters became 42%. How many less male supporters from Sweden than Korea were there at first?

Sweden		Korea
7 u		18 u
Female supporters	Male supporters	Female supporters	Male supporters
1	6	1x3	5x3
1 u	6 u	3 u	15 u

(a)
Number of female supporters from Korea
= ¹₆ x 18 u
= 3 u

Number of male supporters from Sweden
= ⁵₆ x 18 u
= 15 u

Total number of female supporters
= 1 u + 3 u
= 4 u

Female supporters from Sweden : Total female supporters
1 : 4

(b)

	Female supporters	Male supporters
Before	4x2 = 8%	21x2 = 42%
Change	+ 250
After	58%	42%

Number of female supporters in the end in percent
= 100% - 42%
= 58%

Total number of male supporters at first
= 6 u + 15 u
= 21 u

After another 250 female supporters from both countries joined the games, the percentage of all the male supporters became 42%.

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

21 u = 42%

1 u = 42% ÷ 21 = 2%

Number of female supporters at first in percent
= 4 x 2%
= 8%

Number of female supporters from both countries who joined the games
= 58% - 8%
= 50%

50% = 250 

1% = 250 ÷ 50 = 5

Number of less male supporters from Sweden than Korea at first
= 15 u - 6 u
= 9 u
= 9 x 2%
= 18%
= 18 x 5
= 90 

Answer(s): (a) 1 : 4; (b) 90