France and Scotland took part in Youth Games. From France, the ratio of the number of male supporters to the number of female supporters was 1 : 10. From Scotland, the ratio of the number of male supporters to the number of female supporters was 4 : 5. The total number of supporters from France was ¹¹₂₇ the total number of supporters from Scotland.

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 154 male supporters from both countries left the games, the percentage of all the female supporters became 75%. How many more female supporters from Scotland than France were there at first?

France		Scotland
11 u		27 u
Male supporters	Female supporters	Male supporters	Female supporters
1	10	4x3	5x3
1 u	10 u	12 u	15 u

(a)
Number of male supporters from Scotland
= ⁴₉ x 27 u
= 12 u

Number of female supporters from France
= ⁵₉ x 27 u
= 15 u

Total number of male supporters
= 1 u + 12 u
= 13 u

Male supporters from France : Total male supporters
1 : 13

(b)

	Male supporters	Female supporters
Before	13x3 = 39%	25x3 = 75%
Change	- 154
After	25%	75%

Number of male supporters in the end in percent
= 100% - 75%
= 25%

Total number of female supporters at first
= 10 u + 15 u
= 25 u

After 154 male supporters from both countries left the games, the percentage of all the female supporters became 75%.

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

25 u = 75%

1 u = 75% ÷ 25 = 3%

Number of male supporters at first in percent
= 13 x 3%
= 39%

Number of male supporters from both countries who left
= 39% - 25%
= 14%

14% = 154 

1% = 154 ÷ 14 = 11

Number of more female supporters from Scotland than France at first
= 15 u - 10 u
= 5 u
= 5 x 3%
= 15%
= 15 x 11
= 165 

Answer(s): (a) 1 : 13; (b) 165