Egypt and England took part in Youth Games. From Egypt, the ratio of the number of male supporters to the number of female supporters was 1 : 12. From England, the ratio of the number of male supporters to the number of female supporters was 1 : 8. The total number of supporters from Egypt was
1318 the total number of supporters from England.
- 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 another 42 male supporters from both countries joined the games, the percentage of all the female supporters became 84%. How many less female supporters from Egypt than England were there at first?
Egypt |
England |
13 u |
18 u |
Male supporters |
Female supporters |
Male supporters |
Female supporters |
1 |
12 |
1x2 |
8x2 |
1 u |
12 u |
2 u |
16 u |
(a)
Number of male supporters from England
=
19 x 18 u
= 2 u
Number of female supporters from Egypt
=
89 x 18 u
= 16 u
Total number of male supporters
= 1 u + 2 u
= 3 u
Male supporters from Egypt : Total male supporters
1 : 3
(b)
|
Male supporters |
Female supporters |
Before |
3x3 = 9% |
28x3 = 84% |
Change |
+ 42 |
|
After |
16% |
84% |
Number of male supporters in the end in percent
= 100% - 84%
= 16%
Total number of female supporters at first
= 12 u + 16 u
= 28 u
After another 42 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
= 3 x 3%
= 9%
Number of male supporters from both countries who joined the games
= 16% - 9%
= 7%
7% = 42
1% = 42 ÷ 7 =
6Number of less female supporters from Egypt than England at first
= 16 u - 12 u
= 4 u
= 4 x 3%
= 12%
= 12 x 6
= 72
Answer(s): (a) 1 : 3; (b) 72