PSLE At a swimathon, each participant completed either a 3-km route, a 6-km route or a 8-km route.
13 of the participants completed the 3-km route,
49 of the participants completed the 6-km route and the rest completed the 8-km route. For every 1 km a participant swam, $8 was donated to charity. A total of $5880 was donated to charity.
- What is the ratio of the number of participants who completed the 3-km route to the number who completed the 6-km route to the number who completed the 8-km route?
- What is the total number of participants at the swimathon?
(a)
Fraction of the participants who completed 8-km route
= 1 -
13 -
49 = 1 -
39 -
49= 1 -
79 =
29 Ratio of participants who completed the different routes
3 km : 6 km : 8 km
3 : 4 : 2
(b)
For every 1 km a participant swam, $8 was donated to charity.
Total distance covered by the participants
= 5880 ÷ 8
= 735 km
|
3-km |
6-km |
8-km |
Total |
Number |
3 u |
4 u |
2 u |
9 u |
Value |
3 |
6 |
8 |
|
Total value |
9 u |
24 u |
16 u |
|
Total distance that the participants covered
= 3 x 3 u + 6 x 4 u + 8 x 2 u
= 9 u + 24 u + 16 u
= 49 u
49 u = 735
1 u = 735 ÷ 49 = 15
Total number of participants
= 3 u + 4 u + 2 u
= 9 u
= 9 x 15
= 135
Answer(s): (a) 3 : 4 : 2; (b) 135