Japan and Egypt took part in Youth Games. From Japan, the ratio of the number of male supporters to the number of female supporters was 1 : 10. From Egypt, the ratio of the number of male supporters to the number of female supporters was 1 : 3. The total number of supporters from Japan was
1116 the total number of supporters from Egypt.
- What was the ratio of the number of male supporters from Japan to the total number of male supporters from both countries? Express the answer in the simplest form.
- After 72 male supporters from both countries left the games, the percentage of all the female supporters became 88%. How many more female supporters from Egypt than Japan were there at first?
Japan |
Egypt |
11 u |
16 u |
Male supporters |
Female supporters |
Male supporters |
Female supporters |
1 |
10 |
1x2 |
3x2 |
1 u |
10 u |
4 u |
12 u |
(a)
Number of male supporters from Egypt
=
14 x 16 u
= 4 u
Number of female supporters from Japan
=
34 x 16 u
= 12 u
Total number of male supporters
= 1 u + 4 u
= 5 u
Male supporters from Japan : Total male supporters
1 : 5
(b)
|
Male supporters |
Female supporters |
Before |
5x4 = 20% |
22x4 = 88% |
Change |
- 72 |
|
After |
12% |
88% |
Number of male supporters in the end in percent
= 100% - 88%
= 12%
Total number of female supporters at first
= 10 u + 12 u
= 22 u
After 72 male supporters from both countries left the games, the percentage of all the female supporters became 88%.
Since only male supporters left the games, the number of female supporters remains unchanged. Make the number of female supporters the same.
22 u = 88%
1 u = 88% ÷ 22 =
4%Number of male supporters at first in percent
= 5 x 4%
= 20%
Number of male supporters from both countries who left
= 20% - 12%
= 8%
8% = 72
1% = 72 ÷ 8 =
9Number of more female supporters from Egypt than Japan at first
= 12 u - 10 u
= 2 u
= 2 x 4%
= 8%
= 8 x 9
= 72
Answer(s): (a) 1 : 5; (b) 72