Egypt and Jordan took part in Youth Games. From Egypt, the ratio of the number of male supporters to the number of female supporters was 1 : 10. From Jordan, the ratio of the number of male supporters to the number of female supporters was 3 : 5. The total number of supporters from Egypt was
1124 the total number of supporters from Jordan.
- What was the ratio of the number of male supporters from Egypt to the total number of male supporters from both countries? Express the answer in the simplest form.
- After 15 male supporters from both countries left the games, the percentage of all the female supporters became 75%. How many more female supporters from Jordan than Egypt were there at first?
Egypt |
Jordan |
11 u |
24 u |
Male supporters |
Female supporters |
Male supporters |
Female supporters |
1 |
10 |
3x3 |
5x3 |
1 u |
10 u |
9 u |
15 u |
(a)
Number of male supporters from Jordan
=
38 x 24 u
= 9 u
Number of female supporters from Egypt
=
58 x 24 u
= 15 u
Total number of male supporters
= 1 u + 9 u
= 10 u
Male supporters from Egypt : Total male supporters
1 : 10
(b)
|
Male supporters |
Female supporters |
Before |
10x3 = 30% |
25x3 = 75% |
Change |
- 15 |
|
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 15 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
= 10 x 3%
= 30%
Number of male supporters from both countries who left
= 30% - 25%
= 5%
5% = 15
1% = 15 ÷ 5 =
3Number of more female supporters from Jordan than Egypt at first
= 15 u - 10 u
= 5 u
= 5 x 3%
= 15%
= 15 x 3
= 45
Answer(s): (a) 1 : 10; (b) 45