England and Finland took part in Youth Games. From England, the ratio of the number of male supporters to the number of female supporters was 1 : 4. From Finland, the ratio of the number of male supporters to the number of female supporters was 1 : 2. The total number of supporters from England was ⁵₁₂ the total number of supporters from Finland.

1. What was the ratio of the number of male supporters from England to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 396 male supporters from both countries joined the games, the percentage of all the female supporters became 24%. How many less female supporters from England than Finland were there at first?

England		Finland
5 u		12 u
Male supporters	Female supporters	Male supporters	Female supporters
1	4	1x2	2x2
1 u	4 u	4 u	8 u

(a)
Number of male supporters from Finland
= ¹₃ x 12 u
= 4 u

Number of female supporters from England
= ²₃ x 12 u
= 8 u

Total number of male supporters
= 1 u + 4 u
= 5 u

Male supporters from England : Total male supporters
1 : 5

(b)

	Male supporters	Female supporters
Before	5x2 = 10%	12x2 = 24%
Change	+ 396
After	76%	24%

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

Total number of female supporters at first
= 4 u + 8 u
= 12 u

After another 396 male supporters from both countries joined the games, the percentage of all the female supporters became 24%.

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

12 u = 24%

1 u = 24% ÷ 12 = 2%

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

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

66% = 396 

1% = 396 ÷ 66 = 6

Number of less female supporters from England than Finland at first
= 8 u - 4 u
= 4 u
= 4 x 2%
= 8%
= 8 x 6
= 48 

Answer(s): (a) 1 : 5; (b) 48