Canada and Vietnam took part in Youth Games. From Canada, the ratio of the number of male supporters to the number of female supporters was 1 : 6. From Vietnam, the ratio of the number of male supporters to the number of female supporters was 1 : 3. The total number of supporters from Canada was ⁷₂₄ the total number of supporters from Vietnam.

1. What was the ratio of the number of male supporters from Canada to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 418 male supporters from both countries joined the games, the percentage of all the female supporters became 48%. How many less female supporters from Canada than Vietnam were there at first?

Canada		Vietnam
7 u		24 u
Male supporters	Female supporters	Male supporters	Female supporters
1	6	1x2	3x2
1 u	6 u	6 u	18 u

(a)
Number of male supporters from Vietnam
= ¹₄ x 24 u
= 6 u

Number of female supporters from Canada
= ³₄ x 24 u
= 18 u

Total number of male supporters
= 1 u + 6 u
= 7 u

Male supporters from Canada : Total male supporters
1 : 7

(b)

	Male supporters	Female supporters
Before	7x2 = 14%	24x2 = 48%
Change	+ 418
After	52%	48%

Number of male supporters in the end in percent
= 100% - 48%
= 52%

Total number of female supporters at first
= 6 u + 18 u
= 24 u

After another 418 male supporters from both countries joined the games, the percentage of all the female supporters became 48%.

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 = 48%

1 u = 48% ÷ 24 = 2%

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

Number of male supporters from both countries who joined the games
= 52% - 14%
= 38%

38% = 418 

1% = 418 ÷ 38 = 11

Number of less female supporters from Canada than Vietnam at first
= 18 u - 6 u
= 12 u
= 12 x 2%
= 24%
= 24 x 11
= 264 

Answer(s): (a) 1 : 7; (b) 264