Oman and England took part in Youth Games. From Oman, the ratio of the number of male supporters to the number of female supporters was 1 : 6. 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 Oman was ⁷₂₄ the total number of supporters from England.

1. What was the ratio of the number of male supporters from Oman to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After another 418 male supporters from both countries joined the games, the percentage of all the female supporters became 42%. How many less female supporters from Oman than England were there at first?

Oman		England
7 u		24 u
Male supporters	Female supporters	Male supporters	Female supporters
1	6	3x3	5x3
1 u	6 u	9 u	15 u

(a)
Number of male supporters from England
= ³₈ x 24 u
= 9 u

Number of female supporters from Oman
= ⁵₈ x 24 u
= 15 u

Total number of male supporters
= 1 u + 9 u
= 10 u

Male supporters from Oman : Total male supporters
1 : 10

(b)

	Male supporters	Female supporters
Before	10x2 = 20%	21x2 = 42%
Change	+ 418
After	58%	42%

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

Total number of female supporters at first
= 6 u + 15 u
= 21 u

After another 418 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
= 10 x 2%
= 20%

Number of male supporters from both countries who joined the games
= 58% - 20%
= 38%

38% = 418 

1% = 418 ÷ 38 = 11

Number of less female supporters from Oman than England at first
= 15 u - 6 u
= 9 u
= 9 x 2%
= 18%
= 18 x 11
= 198 

Answer(s): (a) 1 : 10; (b) 198