Peru and Korea took part in Youth Games. From Peru, the ratio of the number of male supporters to the number of female supporters was 4 : 7. From Korea, the ratio of the number of male supporters to the number of female supporters was 3 : 5. The total number of supporters from Peru was ¹¹₂₄ the total number of supporters from Korea.

1. What was the ratio of the number of male supporters from Peru to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After 50 male supporters from both countries left the games, the percentage of all the female supporters became 66%. How many more female supporters from Korea than Peru were there at first?

Peru		Korea
11 u		24 u
Male supporters	Female supporters	Male supporters	Female supporters
4	7	3x3	5x3
4 u	7 u	9 u	15 u

(a)
Number of male supporters from Korea
= ³₈ x 24 u
= 9 u

Number of female supporters from Peru
= ⁵₈ x 24 u
= 15 u

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

Male supporters from Peru : Total male supporters
4 : 13

(b)

	Male supporters	Female supporters
Before	13x3 = 39%	22x3 = 66%
Change	- 50
After	34%	66%

Number of male supporters in the end in percent
= 100% - 66%
= 34%

Total number of female supporters at first
= 7 u + 15 u
= 22 u

After 50 male supporters from both countries left the games, the percentage of all the female supporters became 66%.

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

22 u = 66%

1 u = 66% ÷ 22 = 3%

Number of male supporters at first in percent
= 13 x 3%
= 39%

Number of male supporters from both countries who left
= 39% - 34%
= 5%

5% = 50 

1% = 50 ÷ 5 = 10

Number of more female supporters from Korea than Peru at first
= 15 u - 7 u
= 8 u
= 8 x 3%
= 24%
= 24 x 10
= 240 

Answer(s): (a) 4 : 13; (b) 240