Peru and France took part in Youth Games. From Peru, the ratio of the number of male supporters to the number of female supporters was 2 : 9. From France, the ratio of the number of male supporters to the number of female supporters was 1 : 2. The total number of supporters from Peru was
1127 the total number of supporters from France.
- What was the ratio of the number of male supporters from Peru to the total number of male supporters from both countries? Express the answer in the simplest form.
- After 42 male supporters from both countries left the games, the percentage of all the female supporters became 81%. How many more female supporters from France than Peru were there at first?
Peru |
France |
11 u |
27 u |
Male supporters |
Female supporters |
Male supporters |
Female supporters |
2 |
9 |
1x3 |
2x3 |
2 u |
9 u |
9 u |
18 u |
(a)
Number of male supporters from France
=
13 x 27 u
= 9 u
Number of female supporters from Peru
=
23 x 27 u
= 18 u
Total number of male supporters
= 2 u + 9 u
= 11 u
Male supporters from Peru : Total male supporters
2 : 11
(b)
|
Male supporters |
Female supporters |
Before |
11x3 = 33% |
27x3 = 81% |
Change |
- 42 |
|
After |
19% |
81% |
Number of male supporters in the end in percent
= 100% - 81%
= 19%
Total number of female supporters at first
= 9 u + 18 u
= 27 u
After 42 male supporters from both countries left the games, the percentage of all the female supporters became 81%.
Since only male supporters left the games, the number of female supporters remains unchanged. Make the number of female supporters the same.
27 u = 81%
1 u = 81% ÷ 27 =
3%Number of male supporters at first in percent
= 11 x 3%
= 33%
Number of male supporters from both countries who left
= 33% - 19%
= 14%
14% = 42
1% = 42 ÷ 14 =
3Number of more female supporters from France than Peru at first
= 18 u - 9 u
= 9 u
= 9 x 3%
= 27%
= 27 x 3
= 81
Answer(s): (a) 2 : 11; (b) 81