Japan and Turkey took part in Youth Games. From Japan, the ratio of the number of female supporters to the number of male supporters was 3 : 2. From Turkey, the ratio of the number of female supporters to the number of male supporters was 4 : 7. The total number of supporters from Japan was ⁵₂₂ the total number of supporters from Turkey.

1. What was the ratio of the number of female supporters from Japan to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 133 female supporters from both countries joined the games, the percentage of all the male supporters became 48%. How many less male supporters from Japan than Turkey were there at first?

Japan		Turkey
5 u		22 u
Female supporters	Male supporters	Female supporters	Male supporters
3	2	4x2	7x2
3 u	2 u	8 u	14 u

(a)
Number of female supporters from Turkey
= ⁴₁₁ x 22 u
= 8 u

Number of male supporters from Japan
= ⁷₁₁ x 22 u
= 14 u

Total number of female supporters
= 3 u + 8 u
= 11 u

Female supporters from Japan : Total female supporters
3 : 11

(b)

	Female supporters	Male supporters
Before	11x3 = 33%	16x3 = 48%
Change	+ 133
After	52%	48%

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

Total number of male supporters at first
= 2 u + 14 u
= 16 u

After another 133 female supporters from both countries joined the games, the percentage of all the male supporters became 48%.

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

16 u = 48%

1 u = 48% ÷ 16 = 3%

Number of female supporters at first in percent
= 11 x 3%
= 33%

Number of female supporters from both countries who joined the games
= 52% - 33%
= 19%

19% = 133 

1% = 133 ÷ 19 = 7

Number of less male supporters from Japan than Turkey at first
= 14 u - 2 u
= 12 u
= 12 x 3%
= 36%
= 36 x 7
= 252 

Answer(s): (a) 3 : 11; (b) 252