PSLE At a swimathon, each participant completed either a 2-km route, a 5-km route or a 6-km route.
15 of the participants completed the 2-km route,
14 of the participants completed the 5-km route and the rest completed the 6-km route. For every 1 km a participant swam, $10 was donated to charity. A total of $13860 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 5-km route to the number who completed the 6-km route?
- What is the total number of participants at the swimathon?
(a)
Fraction of the participants who completed 6-km route
= 1 -
15 -
14 = 1 -
420 -
520= 1 -
920 =
1120 Ratio of participants who completed the different routes
2 km : 5 km : 6 km
4 : 5 : 11
(b)
For every 1 km a participant swam, $10 was donated to charity.
Total distance covered by the participants
= 13860 ÷ 10
= 1386 km
|
2-km |
5-km |
6-km |
Total |
Number |
4 u |
5 u |
11 u |
20 u |
Value |
2 |
5 |
6 |
|
Total value |
8 u |
25 u |
66 u |
|
Total distance that the participants covered
= 2 x 4 u + 5 x 5 u + 6 x 11 u
= 8 u + 25 u + 66 u
= 99 u
99 u = 1386
1 u = 1386 ÷ 99 = 14
Total number of participants
= 4 u + 5 u + 11 u
= 20 u
= 20 x 14
= 280
Answer(s): (a) 4 : 5 : 11; (b) 280