Egypt and Israel took part in Youth Games. From Egypt, the ratio of the number of male supporters to the number of female supporters was 1 : 4. From Israel, the ratio of the number of male supporters to the number of female supporters was 1 : 7. The total number of supporters from Egypt was ⁵₁₆ the total number of supporters from Israel.

1. What was the ratio of the number of male supporters from Egypt to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 370 male supporters from both countries joined the games, the percentage of all the female supporters became 54%. How many less female supporters from Egypt than Israel were there at first?

Egypt		Israel
5 u		16 u
Male supporters	Female supporters	Male supporters	Female supporters
1	4	1x2	7x2
1 u	4 u	2 u	14 u

(a)
Number of male supporters from Israel
= ¹₈ x 16 u
= 2 u

Number of female supporters from Egypt
= ⁷₈ x 16 u
= 14 u

Total number of male supporters
= 1 u + 2 u
= 3 u

Male supporters from Egypt : Total male supporters
1 : 3

(b)

	Male supporters	Female supporters
Before	3x3 = 9%	18x3 = 54%
Change	+ 370
After	46%	54%

Number of male supporters in the end in percent
= 100% - 54%
= 46%

Total number of female supporters at first
= 4 u + 14 u
= 18 u

After another 370 male supporters from both countries joined the games, the percentage of all the female supporters became 54%.

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

18 u = 54%

1 u = 54% ÷ 18 = 3%

Number of male supporters at first in percent
= 3 x 3%
= 9%

Number of male supporters from both countries who joined the games
= 46% - 9%
= 37%

37% = 370 

1% = 370 ÷ 37 = 10

Number of less female supporters from Egypt than Israel at first
= 14 u - 4 u
= 10 u
= 10 x 3%
= 30%
= 30 x 10
= 300 

Answer(s): (a) 1 : 3; (b) 300