Kenya and Italy took part in Youth Games. From Kenya, the ratio of the number of female supporters to the number of male supporters was 1 : 4. From Italy, the ratio of the number of female supporters to the number of male supporters was 1 : 10. The total number of supporters from Kenya was ⁵₂₂ the total number of supporters from Italy.

1. What was the ratio of the number of female supporters from Kenya to the total number of female supporters from both countries? Express the answer in the simplest form.
2. After another 138 female supporters from both countries joined the games, the percentage of all the male supporters became 48%. How many less male supporters from Kenya than Italy were there at first?

Kenya		Italy
5 u		22 u
Female supporters	Male supporters	Female supporters	Male supporters
1	4	1x2	10x2
1 u	4 u	2 u	20 u

(a)
Number of female supporters from Italy
= ¹₁₁ x 22 u
= 2 u

Number of male supporters from Kenya
= ¹⁰₁₁ x 22 u
= 20 u

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

Female supporters from Kenya : Total female supporters
1 : 3

(b)

	Female supporters	Male supporters
Before	3x2 = 6%	24x2 = 48%
Change	+ 138
After	52%	48%

Number of female supporters in the end in percent
= 100% - 48%
= 52%

Total number of male supporters at first
= 4 u + 20 u
= 24 u

After another 138 female supporters from both countries joined the games, the percentage of all the male supporters became 48%.

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

24 u = 48%

1 u = 48% ÷ 24 = 2%

Number of female supporters at first in percent
= 3 x 2%
= 6%

Number of female supporters from both countries who joined the games
= 52% - 6%
= 46%

46% = 138 

1% = 138 ÷ 46 = 3

Number of less male supporters from Kenya than Italy at first
= 20 u - 4 u
= 16 u
= 16 x 2%
= 32%
= 32 x 3
= 96 

Answer(s): (a) 1 : 3; (b) 96