France and Australia took part in Youth Games. From France, the ratio of the number of male supporters to the number of female supporters was 1 : 9. From Australia, the ratio of the number of male supporters to the number of female supporters was 1 : 8. The total number of supporters from France was ¹⁰₂₇ the total number of supporters from Australia.

1. What was the ratio of the number of male supporters from France to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 52 male supporters from both countries joined the games, the percentage of all the female supporters became 66%. How many less female supporters from France than Australia were there at first?

France		Australia
10 u		27 u
Male supporters	Female supporters	Male supporters	Female supporters
1	9	1x3	8x3
1 u	9 u	3 u	24 u

(a)
Number of male supporters from Australia
= ¹₉ x 27 u
= 3 u

Number of female supporters from France
= ⁸₉ x 27 u
= 24 u

Total number of male supporters
= 1 u + 3 u
= 4 u

Male supporters from France : Total male supporters
1 : 4

(b)

	Male supporters	Female supporters
Before	4x2 = 8%	33x2 = 66%
Change	+ 52
After	34%	66%

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

Total number of female supporters at first
= 9 u + 24 u
= 33 u

After another 52 male supporters from both countries joined the games, the percentage of all the female supporters became 66%.

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

33 u = 66%

1 u = 66% ÷ 33 = 2%

Number of male supporters at first in percent
= 4 x 2%
= 8%

Number of male supporters from both countries who joined the games
= 34% - 8%
= 26%

26% = 52 

1% = 52 ÷ 26 = 2

Number of less female supporters from France than Australia at first
= 24 u - 9 u
= 15 u
= 15 x 2%
= 30%
= 30 x 2
= 60 

Answer(s): (a) 1 : 4; (b) 60