Vietnam and Fiji took part in Youth Games. From Vietnam, the ratio of the number of male supporters to the number of female supporters was 3 : 4. From Fiji, the ratio of the number of male supporters to the number of female supporters was 1 : 5. The total number of supporters from Vietnam was ⁷₂₄ the total number of supporters from Fiji.

1. What was the ratio of the number of male supporters from Vietnam to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 190 male supporters from both countries joined the games, the percentage of all the female supporters became 48%. How many less female supporters from Vietnam than Fiji were there at first?

Vietnam		Fiji
7 u		24 u
Male supporters	Female supporters	Male supporters	Female supporters
3	4	1x2	5x2
3 u	4 u	4 u	20 u

(a)
Number of male supporters from Fiji
= ¹₆ x 24 u
= 4 u

Number of female supporters from Vietnam
= ⁵₆ x 24 u
= 20 u

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

Male supporters from Vietnam : Total male supporters
3 : 7

(b)

	Male supporters	Female supporters
Before	7x2 = 14%	24x2 = 48%
Change	+ 190
After	52%	48%

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

Total number of female supporters at first
= 4 u + 20 u
= 24 u

After another 190 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% = 190 

1% = 190 ÷ 38 = 5

Number of less female supporters from Vietnam than Fiji at first
= 20 u - 4 u
= 16 u
= 16 x 2%
= 32%
= 32 x 5
= 160 

Answer(s): (a) 3 : 7; (b) 160