Brazil and Vietnam took part in Youth Games. From Brazil, the ratio of the number of female supporters to the number of male supporters was 3 : 8. From Vietnam, the ratio of the number of female supporters to the number of male supporters was 1 : 8. The total number of supporters from Brazil was ¹¹₁₈ the total number of supporters from Vietnam.

1. What was the ratio of the number of female supporters from Brazil to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 91 female supporters from both countries joined the games, the percentage of all the male supporters became 72%. How many less male supporters from Brazil than Vietnam were there at first?

Brazil		Vietnam
11 u		18 u
Female supporters	Male supporters	Female supporters	Male supporters
3	8	1x2	8x2
3 u	8 u	2 u	16 u

(a)
Number of female supporters from Vietnam
= ¹₉ x 18 u
= 2 u

Number of male supporters from Brazil
= ⁸₉ x 18 u
= 16 u

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

Female supporters from Brazil : Total female supporters
3 : 5

(b)

	Female supporters	Male supporters
Before	5x3 = 15%	24x3 = 72%
Change	+ 91
After	28%	72%

Number of female supporters in the end in percent
= 100% - 72%
= 28%

Total number of male supporters at first
= 8 u + 16 u
= 24 u

After another 91 female supporters from both countries joined the games, the percentage of all the male supporters became 72%.

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

24 u = 72%

1 u = 72% ÷ 24 = 3%

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

Number of female supporters from both countries who joined the games
= 28% - 15%
= 13%

13% = 91 

1% = 91 ÷ 13 = 7

Number of less male supporters from Brazil than Vietnam at first
= 16 u - 8 u
= 8 u
= 8 x 3%
= 24%
= 24 x 7
= 168 

Answer(s): (a) 3 : 5; (b) 168