Peru and Denmark 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 Denmark, the ratio of the number of male supporters to the number of female supporters was 1 : 2. The total number of supporters from Peru was ¹¹₂₇ the total number of supporters from Denmark.

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 126 male supporters from both countries left the games, the percentage of all the female supporters became 75%. How many more female supporters from Denmark than Peru were there at first?

Peru		Denmark
11 u		27 u
Male supporters	Female supporters	Male supporters	Female supporters
4	7	1x3	2x3
4 u	7 u	9 u	18 u

(a)
Number of male supporters from Denmark
= ¹₃ x 27 u
= 9 u

Number of female supporters from Peru
= ²₃ x 27 u
= 18 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%	25x3 = 75%
Change	- 126
After	25%	75%

Number of male supporters in the end in percent
= 100% - 75%
= 25%

Total number of female supporters at first
= 7 u + 18 u
= 25 u

After 126 male supporters from both countries left the games, the percentage of all the female supporters became 75%.

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

25 u = 75%

1 u = 75% ÷ 25 = 3%

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

Number of male supporters from both countries who left
= 39% - 25%
= 14%

14% = 126 

1% = 126 ÷ 14 = 9

Number of more female supporters from Denmark than Peru at first
= 18 u - 7 u
= 11 u
= 11 x 3%
= 33%
= 33 x 9
= 297 

Answer(s): (a) 4 : 13; (b) 297