Iraq and Canada took part in Youth Games. From Iraq, the ratio of the number of female supporters to the number of male supporters was 4 : 1. From Canada, the ratio of the number of female supporters to the number of male supporters was 1 : 7. The total number of supporters from Iraq was ⁵₂₄ the total number of supporters from Canada.

1. What was the ratio of the number of female supporters from Iraq to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 156 female supporters from both countries joined the games, the percentage of all the male supporters became 66%. How many less male supporters from Iraq than Canada were there at first?

Iraq		Canada
5 u		24 u
Female supporters	Male supporters	Female supporters	Male supporters
4	1	1x3	7x3
4 u	1 u	3 u	21 u

(a)
Number of female supporters from Canada
= ¹₈ x 24 u
= 3 u

Number of male supporters from Iraq
= ⁷₈ x 24 u
= 21 u

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

Female supporters from Iraq : Total female supporters
4 : 7

(b)

	Female supporters	Male supporters
Before	7x3 = 21%	22x3 = 66%
Change	+ 156
After	34%	66%

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

Total number of male supporters at first
= 1 u + 21 u
= 22 u

After another 156 female supporters from both countries joined the games, the percentage of all the male supporters became 66%.

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

22 u = 66%

1 u = 66% ÷ 22 = 3%

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

Number of female supporters from both countries who joined the games
= 34% - 21%
= 13%

13% = 156 

1% = 156 ÷ 13 = 12

Number of less male supporters from Iraq than Canada at first
= 21 u - 1 u
= 20 u
= 20 x 3%
= 60%
= 60 x 12
= 720 

Answer(s): (a) 4 : 7; (b) 720