Australia and Zambia took part in Youth Games. From Australia, the ratio of the number of male supporters to the number of female supporters was 1 : 4. From Zambia, the ratio of the number of male supporters to the number of female supporters was 1 : 8. The total number of supporters from Australia was
527 the total number of supporters from Zambia.
- What was the ratio of the number of male supporters from Australia to the total number of male supporters from both countries? Express the answer in the simplest form.
- After another 36 male supporters from both countries joined the games, the percentage of all the female supporters became 84%. How many less female supporters from Australia than Zambia were there at first?
Australia |
Zambia |
5 u |
27 u |
Male supporters |
Female supporters |
Male supporters |
Female supporters |
1 |
4 |
1x3 |
8x3 |
1 u |
4 u |
3 u |
24 u |
(a)
Number of male supporters from Zambia
=
19 x 27 u
= 3 u
Number of female supporters from Australia
=
89 x 27 u
= 24 u
Total number of male supporters
= 1 u + 3 u
= 4 u
Male supporters from Australia : Total male supporters
1 : 4
(b)
|
Male supporters |
Female supporters |
Before |
4x3 = 12% |
28x3 = 84% |
Change |
+ 36 |
|
After |
16% |
84% |
Number of male supporters in the end in percent
= 100% - 84%
= 16%
Total number of female supporters at first
= 4 u + 24 u
= 28 u
After another 36 male supporters from both countries joined the games, the percentage of all the female supporters became 84%.
Since only more male supporters joined the games, the number of female supporters remains unchanged. Make the number of female supporters the same.
28 u = 84%
1 u = 84% ÷ 28 =
3%Number of male supporters at first in percent
= 4 x 3%
= 12%
Number of male supporters from both countries who joined the games
= 16% - 12%
= 4%
4% = 36
1% = 36 ÷ 4 =
9Number of less female supporters from Australia than Zambia at first
= 24 u - 4 u
= 20 u
= 20 x 3%
= 60%
= 60 x 9
= 540
Answer(s): (a) 1 : 4; (b) 540