Italy and England took part in Youth Games. From Italy, the ratio of the number of male supporters to the number of female supporters was 1 : 4. From England, the ratio of the number of male supporters to the number of female supporters was 3 : 5. The total number of supporters from Italy was ⁵₁₆ the total number of supporters from England.

1. What was the ratio of the number of male supporters from Italy to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 333 male supporters from both countries joined the games, the percentage of all the female supporters became 42%. How many less female supporters from Italy than England were there at first?

Italy		England
5 u		16 u
Male supporters	Female supporters	Male supporters	Female supporters
1	4	3x2	5x2
1 u	4 u	6 u	10 u

(a)
Number of male supporters from England
= ³₈ x 16 u
= 6 u

Number of female supporters from Italy
= ⁵₈ x 16 u
= 10 u

Total number of male supporters
= 1 u + 6 u
= 7 u

Male supporters from Italy : Total male supporters
1 : 7

(b)

	Male supporters	Female supporters
Before	7x3 = 21%	14x3 = 42%
Change	+ 333
After	58%	42%

Number of male supporters in the end in percent
= 100% - 42%
= 58%

Total number of female supporters at first
= 4 u + 10 u
= 14 u

After another 333 male supporters from both countries joined the games, the percentage of all the female supporters became 42%.

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

14 u = 42%

1 u = 42% ÷ 14 = 3%

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

Number of male supporters from both countries who joined the games
= 58% - 21%
= 37%

37% = 333 

1% = 333 ÷ 37 = 9

Number of less female supporters from Italy than England at first
= 10 u - 4 u
= 6 u
= 6 x 3%
= 18%
= 18 x 9
= 162 

Answer(s): (a) 1 : 7; (b) 162