PSLE At a swimathon, each participant completed either a 2-km route, a 4-km route or a 5-km route.
14 of the participants completed the 2-km route,
57 of the participants completed the 4-km route and the rest completed the 5-km route. For every 1 km a participant swam, $6 was donated to charity. A total of $11880 was donated to charity.
- What is the ratio of the number of participants who completed the 2-km route to the number who completed the 4-km route to the number who completed the 5-km route?
- What is the total number of participants at the swimathon?
(a)
Fraction of the participants who completed 5-km route
= 1 -
14 -
57 = 1 -
728 -
2028= 1 -
2728 =
128 Ratio of participants who completed the different routes
2 km : 4 km : 5 km
7 : 20 : 1
(b)
For every 1 km a participant swam, $6 was donated to charity.
Total distance covered by the participants
= 11880 ÷ 6
= 1980 km
|
2-km |
4-km |
5-km |
Total |
Number |
7 u |
20 u |
1 u |
28 u |
Value |
2 |
4 |
5 |
|
Total value |
14 u |
80 u |
5 u |
|
Total distance that the participants covered
= 2 x 7 u + 4 x 20 u + 5 x 1 u
= 14 u + 80 u + 5 u
= 99 u
99 u = 1980
1 u = 1980 ÷ 99 = 20
Total number of participants
= 7 u + 20 u + 1 u
= 28 u
= 28 x 20
= 560
Answer(s): (a) 7 : 20 : 1; (b) 560