PSLE At a swimathon, each participant completed either a 2-km route, a 3-km route or a 5-km route.
12 of the participants completed the 2-km route,
13 of the participants completed the 3-km route and the rest completed the 5-km route. For every 1 km a participant swam, $10 was donated to charity. A total of $3060 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 3-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 -
12 -
13 = 1 -
36 -
26= 1 -
56 =
16 Ratio of participants who completed the different routes
2 km : 3 km : 5 km
3 : 2 : 1
(b)
For every 1 km a participant swam, $10 was donated to charity.
Total distance covered by the participants
= 3060 ÷ 10
= 306 km
|
2-km |
3-km |
5-km |
Total |
Number |
3 u |
2 u |
1 u |
6 u |
Value |
2 |
3 |
5 |
|
Total value |
6 u |
6 u |
5 u |
|
Total distance that the participants covered
= 2 x 3 u + 3 x 2 u + 5 x 1 u
= 6 u + 6 u + 5 u
= 17 u
17 u = 306
1 u = 306 ÷ 17 = 18
Total number of participants
= 3 u + 2 u + 1 u
= 6 u
= 6 x 18
= 108
Answer(s): (a) 3 : 2 : 1; (b) 108