PSLE At a swimathon, each participant completed either a 1-km route, a 3-km route or a 6-km route.
16 of the participants completed the 1-km route,
59 of the participants completed the 3-km route and the rest completed the 6-km route. For every 1 km a participant swam, $8 was donated to charity. A total of $9072 was donated to charity.
- What is the ratio of the number of participants who completed the 1-km route to the number who completed the 3-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 -
16 -
59 = 1 -
318 -
1018= 1 -
1318 =
518 Ratio of participants who completed the different routes
1 km : 3 km : 6 km
3 : 10 : 5
(b)
For every 1 km a participant swam, $8 was donated to charity.
Total distance covered by the participants
= 9072 ÷ 8
= 1134 km
|
1-km |
3-km |
6-km |
Total |
Number |
3 u |
10 u |
5 u |
18 u |
Value |
1 |
3 |
6 |
|
Total value |
3 u |
30 u |
30 u |
|
Total distance that the participants covered
= 1 x 3 u + 3 x 10 u + 6 x 5 u
= 3 u + 30 u + 30 u
= 63 u
63 u = 1134
1 u = 1134 ÷ 63 = 18
Total number of participants
= 3 u + 10 u + 5 u
= 18 u
= 18 x 18
= 324
Answer(s): (a) 3 : 10 : 5; (b) 324