Scotland and Malta took part in Youth Games. From Scotland, the ratio of the number of male supporters to the number of female supporters was 4 : 7. From Malta, the ratio of the number of male supporters to the number of female supporters was 3 : 5. The total number of supporters from Scotland was
1124 the total number of supporters from Malta.
- 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.
- After 55 male supporters from both countries left the games, the percentage of all the female supporters became 66%. How many more female supporters from Malta than Scotland were there at first?
Scotland |
Malta |
11 u |
24 u |
Male supporters |
Female supporters |
Male supporters |
Female supporters |
4 |
7 |
3x3 |
5x3 |
4 u |
7 u |
9 u |
15 u |
(a)
Number of male supporters from Malta
=
38 x 24 u
= 9 u
Number of female supporters from Scotland
=
58 x 24 u
= 15 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 |
13x3 = 39% |
22x3 = 66% |
Change |
- 55 |
|
After |
34% |
66% |
Number of male supporters in the end in percent
= 100% - 66%
= 34%
Total number of female supporters at first
= 7 u + 15 u
= 22 u
After 55 male supporters from both countries left the games, the percentage of all the female supporters became 66%.
Since only male supporters left the games, the number of female supporters remains unchanged. Make the number of female supporters the same.
22 u = 66%
1 u = 66% ÷ 22 =
3%Number of male supporters at first in percent
= 13 x 3%
= 39%
Number of male supporters from both countries who left
= 39% - 34%
= 5%
5% = 55
1% = 55 ÷ 5 =
11Number of more female supporters from Malta than Scotland at first
= 15 u - 7 u
= 8 u
= 8 x 3%
= 24%
= 24 x 11
= 264
Answer(s): (a) 4 : 13; (b) 264