Haiti and Korea took part in Youth Games. From Haiti, the ratio of the number of female supporters to the number of male supporters was 3 : 2. From Korea, the ratio of the number of female supporters to the number of male supporters was 1 : 3. The total number of supporters from Haiti was ⁵₈ the total number of supporters from Korea.

1. What was the ratio of the number of female supporters from Haiti to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 384 female supporters from both countries joined the games, the percentage of all the male supporters became 32%. How many less male supporters from Haiti than Korea were there at first?

Haiti		Korea
5 u		8 u
Female supporters	Male supporters	Female supporters	Male supporters
3	2	1x2	3x2
3 u	2 u	2 u	6 u

(a)
Number of female supporters from Korea
= ¹₄ x 8 u
= 2 u

Number of male supporters from Haiti
= ³₄ x 8 u
= 6 u

Total number of female supporters
= 3 u + 2 u
= 5 u

Female supporters from Haiti : Total female supporters
3 : 5

(b)

	Female supporters	Male supporters
Before	5x4 = 20%	8x4 = 32%
Change	+ 384
After	68%	32%

Number of female supporters in the end in percent
= 100% - 32%
= 68%

Total number of male supporters at first
= 2 u + 6 u
= 8 u

After another 384 female supporters from both countries joined the games, the percentage of all the male supporters became 32%.

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

8 u = 32%

1 u = 32% ÷ 8 = 4%

Number of female supporters at first in percent
= 5 x 4%
= 20%

Number of female supporters from both countries who joined the games
= 68% - 20%
= 48%

48% = 384 

1% = 384 ÷ 48 = 8

Number of less male supporters from Haiti than Korea at first
= 6 u - 2 u
= 4 u
= 4 x 4%
= 16%
= 16 x 8
= 128 

Answer(s): (a) 3 : 5; (b) 128