Scotland and Thailand took part in Youth Games. From Scotland, the ratio of the number of male supporters to the number of female supporters was 4 : 3. From Thailand, the ratio of the number of male supporters to the number of female supporters was 1 : 2. The total number of supporters from Scotland was ⁷₂₇ the total number of supporters from Thailand.

1. What was the ratio of the number of male supporters from Scotland to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 128 male supporters from both countries joined the games, the percentage of all the female supporters became 42%. How many less female supporters from Scotland than Thailand were there at first?

Scotland		Thailand
7 u		27 u
Male supporters	Female supporters	Male supporters	Female supporters
4	3	1x3	2x3
4 u	3 u	9 u	18 u

(a)
Number of male supporters from Thailand
= ¹₃ x 27 u
= 9 u

Number of female supporters from Scotland
= ²₃ x 27 u
= 18 u

Total number of male supporters
= 4 u + 9 u
= 13 u

Male supporters from Scotland : Total male supporters
4 : 13

(b)

	Male supporters	Female supporters
Before	13x2 = 26%	21x2 = 42%
Change	+ 128
After	58%	42%

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

Total number of female supporters at first
= 3 u + 18 u
= 21 u

After another 128 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.

21 u = 42%

1 u = 42% ÷ 21 = 2%

Number of male supporters at first in percent
= 13 x 2%
= 26%

Number of male supporters from both countries who joined the games
= 58% - 26%
= 32%

32% = 128 

1% = 128 ÷ 32 = 4

Number of less female supporters from Scotland than Thailand at first
= 18 u - 3 u
= 15 u
= 15 x 2%
= 30%
= 30 x 4
= 120 

Answer(s): (a) 4 : 13; (b) 120