France and Pakistan took part in Youth Games. From France, the ratio of the number of female supporters to the number of male supporters was 3 : 2. From Pakistan, the ratio of the number of female supporters to the number of male supporters was 1 : 2. The total number of supporters from France was
524 the total number of supporters from Pakistan.
- What was the ratio of the number of female supporters from France to the total number of female supporters from both countries? Express the answer in the simplest form.
- After another 143 female supporters from both countries joined the games, the percentage of all the male supporters became 54%. How many less male supporters from France than Pakistan were there at first?
France |
Pakistan |
5 u |
24 u |
Female supporters |
Male supporters |
Female supporters |
Male supporters |
3 |
2 |
1x2 |
2x2 |
3 u |
2 u |
8 u |
16 u |
(a)
Number of female supporters from Pakistan
=
13 x 24 u
= 8 u
Number of male supporters from France
=
23 x 24 u
= 16 u
Total number of female supporters
= 3 u + 8 u
= 11 u
Female supporters from France : Total female supporters
3 : 11
(b)
|
Female supporters |
Male supporters |
Before |
11x3 = 33% |
18x3 = 54% |
Change |
+ 143 |
|
After |
46% |
54% |
Number of female supporters in the end in percent
= 100% - 54%
= 46%
Total number of male supporters at first
= 2 u + 16 u
= 18 u
After another 143 female supporters from both countries joined the games, the percentage of all the male supporters became 54%.
Since only more female supporters joined the games, the number of male supporters remains unchanged. Make the number of male supporters the same.
18 u = 54%
1 u = 54% ÷ 18 =
3%Number of female supporters at first in percent
= 11 x 3%
= 33%
Number of female supporters from both countries who joined the games
= 46% - 33%
= 13%
13% = 143
1% = 143 ÷ 13 =
11Number of less male supporters from France than Pakistan at first
= 16 u - 2 u
= 14 u
= 14 x 3%
= 42%
= 42 x 11
= 462
Answer(s): (a) 3 : 11; (b) 462