PSLE At a swimathon, each participant completed either a 3-km route, a 5-km route or a 6-km route.
14 of the participants completed the 3-km route,
23 of the participants completed the 5-km route and the rest completed the 6-km route. For every 1 km a participant swam, $5 was donated to charity. A total of $5225 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 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 -
14 -
23 = 1 -
312 -
812= 1 -
1112 =
112 Ratio of participants who completed the different routes
3 km : 5 km : 6 km
3 : 8 : 1
(b)
For every 1 km a participant swam, $5 was donated to charity.
Total distance covered by the participants
= 5225 ÷ 5
= 1045 km
|
3-km |
5-km |
6-km |
Total |
Number |
3 u |
8 u |
1 u |
12 u |
Value |
3 |
5 |
6 |
|
Total value |
9 u |
40 u |
6 u |
|
Total distance that the participants covered
= 3 x 3 u + 5 x 8 u + 6 x 1 u
= 9 u + 40 u + 6 u
= 55 u
55 u = 1045
1 u = 1045 ÷ 55 = 19
Total number of participants
= 3 u + 8 u + 1 u
= 12 u
= 12 x 19
= 228
Answer(s): (a) 3 : 8 : 1; (b) 228