China and Russia took part in Youth Games. From China, the ratio of the number of female supporters to the number of male supporters was 3 : 2. From Russia, the ratio of the number of female supporters to the number of male supporters was 1 : 5. The total number of supporters from China was ⁵₂₄ the total number of supporters from Russia.

1. What was the ratio of the number of female supporters from China to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 168 female supporters from both countries joined the games, the percentage of all the male supporters became 44%. How many less male supporters from China than Russia were there at first?

China		Russia
5 u		24 u
Female supporters	Male supporters	Female supporters	Male supporters
3	2	1x2	5x2
3 u	2 u	4 u	20 u

(a)
Number of female supporters from Russia
= ¹₆ x 24 u
= 4 u

Number of male supporters from China
= ⁵₆ x 24 u
= 20 u

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

Female supporters from China : Total female supporters
3 : 7

(b)

	Female supporters	Male supporters
Before	7x2 = 14%	22x2 = 44%
Change	+ 168
After	56%	44%

Number of female supporters in the end in percent
= 100% - 44%
= 56%

Total number of male supporters at first
= 2 u + 20 u
= 22 u

After another 168 female supporters from both countries joined the games, the percentage of all the male supporters became 44%.

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

22 u = 44%

1 u = 44% ÷ 22 = 2%

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

Number of female supporters from both countries who joined the games
= 56% - 14%
= 42%

42% = 168 

1% = 168 ÷ 42 = 4

Number of less male supporters from China than Russia at first
= 20 u - 2 u
= 18 u
= 18 x 2%
= 36%
= 36 x 4
= 144 

Answer(s): (a) 3 : 7; (b) 144