Mexico and Vietnam took part in Youth Games. From Mexico, the ratio of the number of male supporters to the number of female supporters was 4 : 7. From Vietnam, the ratio of the number of male supporters to the number of female supporters was 3 : 4. The total number of supporters from Mexico was ¹¹₂₁ the total number of supporters from Vietnam.

1. What was the ratio of the number of male supporters from Mexico to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 180 male supporters from both countries joined the games, the percentage of all the female supporters became 38%. How many less female supporters from Mexico than Vietnam were there at first?

Mexico		Vietnam
11 u		21 u
Male supporters	Female supporters	Male supporters	Female supporters
4	7	3x3	4x3
4 u	7 u	9 u	12 u

(a)
Number of male supporters from Vietnam
= ³₇ x 21 u
= 9 u

Number of female supporters from Mexico
= ⁴₇ x 21 u
= 12 u

Total number of male supporters
= 4 u + 9 u
= 13 u

Male supporters from Mexico : Total male supporters
4 : 13

(b)

	Male supporters	Female supporters
Before	13x2 = 26%	19x2 = 38%
Change	+ 180
After	62%	38%

Number of male supporters in the end in percent
= 100% - 38%
= 62%

Total number of female supporters at first
= 7 u + 12 u
= 19 u

After another 180 male supporters from both countries joined the games, the percentage of all the female supporters became 38%.

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

19 u = 38%

1 u = 38% ÷ 19 = 2%

Number of male supporters at first in percent
= 13 x 2%
= 26%

Number of male supporters from both countries who joined the games
= 62% - 26%
= 36%

36% = 180 

1% = 180 ÷ 36 = 5

Number of less female supporters from Mexico than Vietnam at first
= 12 u - 7 u
= 5 u
= 5 x 2%
= 10%
= 10 x 5
= 50 

Answer(s): (a) 4 : 13; (b) 50