Greece and Zambia took part in Youth Games. From Greece, the ratio of the number of male supporters to the number of female supporters was 3 : 4. From Zambia, the ratio of the number of male supporters to the number of female supporters was 1 : 9. The total number of supporters from Greece was
720 the total number of supporters from Zambia.
- What was the ratio of the number of male supporters from Greece to the total number of male supporters from both countries? Express the answer in the simplest form.
- After 88 male supporters from both countries left the games, the percentage of all the female supporters became 88%. How many more female supporters from Zambia than Greece were there at first?
Greece |
Zambia |
7 u |
20 u |
Male supporters |
Female supporters |
Male supporters |
Female supporters |
3 |
4 |
1x2 |
9x2 |
3 u |
4 u |
2 u |
18 u |
(a)
Number of male supporters from Zambia
=
110 x 20 u
= 2 u
Number of female supporters from Greece
=
910 x 20 u
= 18 u
Total number of male supporters
= 3 u + 2 u
= 5 u
Male supporters from Greece : Total male supporters
3 : 5
(b)
|
Male supporters |
Female supporters |
Before |
5x4 = 20% |
22x4 = 88% |
Change |
- 88 |
|
After |
12% |
88% |
Number of male supporters in the end in percent
= 100% - 88%
= 12%
Total number of female supporters at first
= 4 u + 18 u
= 22 u
After 88 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% = 88
1% = 88 ÷ 8 =
11Number of more female supporters from Zambia than Greece at first
= 18 u - 4 u
= 14 u
= 14 x 4%
= 56%
= 56 x 11
= 616
Answer(s): (a) 3 : 5; (b) 616