Mexico and Oman took part in Youth Games. From Mexico, the ratio of the number of male supporters to the number of female supporters was 3 : 8. From Oman, the ratio of the number of male supporters to the number of female supporters was 1 : 7. The total number of supporters from Mexico was
1116 the total number of supporters from Oman.
- What was the ratio of the number of male supporters from Mexico to the total number of male supporters from both countries? Express the answer in the simplest form.
- After 96 male supporters from both countries left the games, the percentage of all the female supporters became 88%. How many more female supporters from Oman than Mexico were there at first?
Mexico |
Oman |
11 u |
16 u |
Male supporters |
Female supporters |
Male supporters |
Female supporters |
3 |
8 |
1x2 |
7x2 |
3 u |
8 u |
2 u |
14 u |
(a)
Number of male supporters from Oman
=
18 x 16 u
= 2 u
Number of female supporters from Mexico
=
78 x 16 u
= 14 u
Total number of male supporters
= 3 u + 2 u
= 5 u
Male supporters from Mexico : Total male supporters
3 : 5
(b)
|
Male supporters |
Female supporters |
Before |
5x4 = 20% |
22x4 = 88% |
Change |
- 96 |
|
After |
12% |
88% |
Number of male supporters in the end in percent
= 100% - 88%
= 12%
Total number of female supporters at first
= 8 u + 14 u
= 22 u
After 96 male supporters from both countries left the games, the percentage of all the female supporters became 88%.
Since only male supporters left the games, the number of female supporters remains unchanged. Make the number of female supporters the same.
22 u = 88%
1 u = 88% ÷ 22 =
4%Number of male supporters at first in percent
= 5 x 4%
= 20%
Number of male supporters from both countries who left
= 20% - 12%
= 8%
8% = 96
1% = 96 ÷ 8 =
12Number of more female supporters from Oman than Mexico at first
= 14 u - 8 u
= 6 u
= 6 x 4%
= 24%
= 24 x 12
= 288
Answer(s): (a) 3 : 5; (b) 288