Mexico and Japan took part in Youth Games. From Mexico, the ratio of the number of female supporters to the number of male supporters was 2 : 3. From Japan, the ratio of the number of female supporters to the number of male supporters was 1 : 2. The total number of supporters from Mexico was ⁵₉ the total number of supporters from Japan.

1. What was the ratio of the number of female supporters from Mexico to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 638 female supporters from both countries joined the games, the percentage of all the male supporters became 27%. How many less male supporters from Mexico than Japan were there at first?

Mexico		Japan
5 u		9 u
Female supporters	Male supporters	Female supporters	Male supporters
2	3	1x3	2x3
2 u	3 u	3 u	6 u

(a)
Number of female supporters from Japan
= ¹₃ x 9 u
= 3 u

Number of male supporters from Mexico
= ²₃ x 9 u
= 6 u

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

Female supporters from Mexico : Total female supporters
2 : 5

(b)

	Female supporters	Male supporters
Before	5x3 = 15%	9x3 = 27%
Change	+ 638
After	73%	27%

Number of female supporters in the end in percent
= 100% - 27%
= 73%

Total number of male supporters at first
= 3 u + 6 u
= 9 u

After another 638 female supporters from both countries joined the games, the percentage of all the male supporters became 27%.

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

9 u = 27%

1 u = 27% ÷ 9 = 3%

Number of female supporters at first in percent
= 5 x 3%
= 15%

Number of female supporters from both countries who joined the games
= 73% - 15%
= 58%

58% = 638 

1% = 638 ÷ 58 = 11

Number of less male supporters from Mexico than Japan at first
= 6 u - 3 u
= 3 u
= 3 x 3%
= 9%
= 9 x 11
= 99 

Answer(s): (a) 2 : 5; (b) 99