Peru and Denmark took part in Youth Games. From Peru, the ratio of the number of male supporters to the number of female supporters was 4 : 7. From Denmark, 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 Denmark.
- 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 126 male supporters from both countries left the games, the percentage of all the female supporters became 75%. How many more female supporters from Denmark than Peru were there at first?
Peru |
Denmark |
11 u |
27 u |
Male supporters |
Female supporters |
Male supporters |
Female supporters |
4 |
7 |
1x3 |
2x3 |
4 u |
7 u |
9 u |
18 u |
(a)
Number of male supporters from Denmark
=
13 x 27 u
= 9 u
Number of female supporters from Peru
=
23 x 27 u
= 18 u
Total number of male supporters
= 4 u + 9 u
= 13 u
Male supporters from Peru : Total male supporters
4 : 13
(b)
|
Male supporters |
Female supporters |
Before |
13x3 = 39% |
25x3 = 75% |
Change |
- 126 |
|
After |
25% |
75% |
Number of male supporters in the end in percent
= 100% - 75%
= 25%
Total number of female supporters at first
= 7 u + 18 u
= 25 u
After 126 male supporters from both countries left the games, the percentage of all the female supporters became 75%.
Since only male supporters left the games, the number of female supporters remains unchanged. Make the number of female supporters the same.
25 u = 75%
1 u = 75% ÷ 25 =
3%Number of male supporters at first in percent
= 13 x 3%
= 39%
Number of male supporters from both countries who left
= 39% - 25%
= 14%
14% = 126
1% = 126 ÷ 14 =
9Number of more female supporters from Denmark than Peru at first
= 18 u - 7 u
= 11 u
= 11 x 3%
= 33%
= 33 x 9
= 297
Answer(s): (a) 4 : 13; (b) 297