England and Mexico took part in Youth Games. From England, the ratio of the number of male supporters to the number of female supporters was 3 : 2. From Mexico, the ratio of the number of male supporters to the number of female supporters was 2 : 9. The total number of supporters from England was ⁵₂₂ the total number of supporters from Mexico.

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 414 male supporters from both countries joined the games, the percentage of all the female supporters became 40%. How many less female supporters from England than Mexico were there at first?

England		Mexico
5 u		22 u
Male supporters	Female supporters	Male supporters	Female supporters
3	2	2x2	9x2
3 u	2 u	4 u	18 u

(a)
Number of male supporters from Mexico
= ²₁₁ x 22 u
= 4 u

Number of female supporters from England
= ⁹₁₁ x 22 u
= 18 u

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

Male supporters from England : Total male supporters
3 : 7

(b)

	Male supporters	Female supporters
Before	7x2 = 14%	20x2 = 40%
Change	+ 414
After	60%	40%

Number of male supporters in the end in percent
= 100% - 40%
= 60%

Total number of female supporters at first
= 2 u + 18 u
= 20 u

After another 414 male supporters from both countries joined the games, the percentage of all the female supporters became 40%.

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

20 u = 40%

1 u = 40% ÷ 20 = 2%

Number of male supporters at first in percent
= 7 x 2%
= 14%

Number of male supporters from both countries who joined the games
= 60% - 14%
= 46%

46% = 414 

1% = 414 ÷ 46 = 9

Number of less female supporters from England than Mexico at first
= 18 u - 2 u
= 16 u
= 16 x 2%
= 32%
= 32 x 9
= 288 

Answer(s): (a) 3 : 7; (b) 288