England and Israel took part in Youth Games. From England, the ratio of the number of female supporters to the number of male supporters was 1 : 12. From Israel, the ratio of the number of female supporters to the number of male supporters was 1 : 5. The total number of supporters from England was ¹³₁₈ the total number of supporters from Israel.

1. What was the ratio of the number of female supporters from England to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 49 female supporters from both countries joined the games, the percentage of all the male supporters became 81%. How many less male supporters from England than Israel were there at first?

England		Israel
13 u		18 u
Female supporters	Male supporters	Female supporters	Male supporters
1	12	1x3	5x3
1 u	12 u	3 u	15 u

(a)
Number of female supporters from Israel
= ¹₆ x 18 u
= 3 u

Number of male supporters from England
= ⁵₆ x 18 u
= 15 u

Total number of female supporters
= 1 u + 3 u
= 4 u

Female supporters from England : Total female supporters
1 : 4

(b)

	Female supporters	Male supporters
Before	4x3 = 12%	27x3 = 81%
Change	+ 49
After	19%	81%

Number of female supporters in the end in percent
= 100% - 81%
= 19%

Total number of male supporters at first
= 12 u + 15 u
= 27 u

After another 49 female supporters from both countries joined the games, the percentage of all the male supporters became 81%.

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

27 u = 81%

1 u = 81% ÷ 27 = 3%

Number of female supporters at first in percent
= 4 x 3%
= 12%

Number of female supporters from both countries who joined the games
= 19% - 12%
= 7%

7% = 49 

1% = 49 ÷ 7 = 7

Number of less male supporters from England than Israel at first
= 15 u - 12 u
= 3 u
= 3 x 3%
= 9%
= 9 x 7
= 63 

Answer(s): (a) 1 : 4; (b) 63