Peru and Israel took part in Youth Games. From Peru, the ratio of the number of male supporters to the number of female supporters was 3 : 8. From Israel, the ratio of the number of male supporters to the number of female supporters was 1 : 5. The total number of supporters from Peru was ¹¹₂₄ the total number of supporters from Israel.

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 15 male supporters from both countries left the games, the percentage of all the female supporters became 84%. How many more female supporters from Israel than Peru were there at first?

Peru		Israel
11 u		24 u
Male supporters	Female supporters	Male supporters	Female supporters
3	8	1x2	5x2
3 u	8 u	4 u	20 u

(a)
Number of male supporters from Israel
= ¹₆ x 24 u
= 4 u

Number of female supporters from Peru
= ⁵₆ x 24 u
= 20 u

Total number of male supporters
= 3 u + 4 u
= 7 u

Male supporters from Peru : Total male supporters
3 : 7

(b)

	Male supporters	Female supporters
Before	7x3 = 21%	28x3 = 84%
Change	- 15
After	16%	84%

Number of male supporters in the end in percent
= 100% - 84%
= 16%

Total number of female supporters at first
= 8 u + 20 u
= 28 u

After 15 male supporters from both countries left the games, the percentage of all the female supporters became 84%.

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

28 u = 84%

1 u = 84% ÷ 28 = 3%

Number of male supporters at first in percent
= 7 x 3%
= 21%

Number of male supporters from both countries who left
= 21% - 16%
= 5%

5% = 15 

1% = 15 ÷ 5 = 3

Number of more female supporters from Israel than Peru at first
= 20 u - 8 u
= 12 u
= 12 x 3%
= 36%
= 36 x 3
= 108 

Answer(s): (a) 3 : 7; (b) 108