Ireland and Belgium took part in Youth Games. From Ireland, the ratio of the number of male supporters to the number of female supporters was 3 : 4. From Belgium, the ratio of the number of male supporters to the number of female supporters was 1 : 7. The total number of supporters from Ireland was ⁷₁₆ the total number of supporters from Belgium.

1. What was the ratio of the number of male supporters from Ireland to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 486 male supporters from both countries joined the games, the percentage of all the female supporters became 36%. How many less female supporters from Ireland than Belgium were there at first?

Ireland		Belgium
7 u		16 u
Male supporters	Female supporters	Male supporters	Female supporters
3	4	1x2	7x2
3 u	4 u	2 u	14 u

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

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

Total number of male supporters
= 3 u + 2 u
= 5 u

Male supporters from Ireland : Total male supporters
3 : 5

(b)

	Male supporters	Female supporters
Before	5x2 = 10%	18x2 = 36%
Change	+ 486
After	64%	36%

Number of male supporters in the end in percent
= 100% - 36%
= 64%

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

After another 486 male supporters from both countries joined the games, the percentage of all the female supporters became 36%.

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 = 36%

1 u = 36% ÷ 18 = 2%

Number of male supporters at first in percent
= 5 x 2%
= 10%

Number of male supporters from both countries who joined the games
= 64% - 10%
= 54%

54% = 486 

1% = 486 ÷ 54 = 9

Number of less female supporters from Ireland than Belgium at first
= 14 u - 4 u
= 10 u
= 10 x 2%
= 20%
= 20 x 9
= 180 

Answer(s): (a) 3 : 5; (b) 180