PSLE At a swimathon, each participant completed either a 2-km route, a 5-km route or a 7-km route.
14 of the participants completed the 2-km route,
35 of the participants completed the 5-km route and the rest completed the 7-km route. For every 1 km a participant swam, $6 was donated to charity. A total of $8190 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 7-km route?
- What is the total number of participants at the swimathon?
(a)
Fraction of the participants who completed 7-km route
= 1 -
14 -
35 = 1 -
520 -
1220= 1 -
1720 =
320 Ratio of participants who completed the different routes
2 km : 5 km : 7 km
5 : 12 : 3
(b)
For every 1 km a participant swam, $6 was donated to charity.
Total distance covered by the participants
= 8190 ÷ 6
= 1365 km
|
2-km |
5-km |
7-km |
Total |
Number |
5 u |
12 u |
3 u |
20 u |
Value |
2 |
5 |
7 |
|
Total value |
10 u |
60 u |
21 u |
|
Total distance that the participants covered
= 2 x 5 u + 5 x 12 u + 7 x 3 u
= 10 u + 60 u + 21 u
= 91 u
91 u = 1365
1 u = 1365 ÷ 91 = 15
Total number of participants
= 5 u + 12 u + 3 u
= 20 u
= 20 x 15
= 300
Answer(s): (a) 5 : 12 : 3; (b) 300