PSLE At a swimathon, each participant completed either a 3-km route, a 4-km route or a 7-km route.
12 of the participants completed the 3-km route,
13 of the participants completed the 4-km route and the rest completed the 7-km route. For every 1 km a participant swam, $7 was donated to charity. A total of $2184 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 4-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 -
12 -
13 = 1 -
36 -
26= 1 -
56 =
16 Ratio of participants who completed the different routes
3 km : 4 km : 7 km
3 : 2 : 1
(b)
For every 1 km a participant swam, $7 was donated to charity.
Total distance covered by the participants
= 2184 ÷ 7
= 312 km
|
3-km |
4-km |
7-km |
Total |
Number |
3 u |
2 u |
1 u |
6 u |
Value |
3 |
4 |
7 |
|
Total value |
9 u |
8 u |
7 u |
|
Total distance that the participants covered
= 3 x 3 u + 4 x 2 u + 7 x 1 u
= 9 u + 8 u + 7 u
= 24 u
24 u = 312
1 u = 312 ÷ 24 = 13
Total number of participants
= 3 u + 2 u + 1 u
= 6 u
= 6 x 13
= 78
Answer(s): (a) 3 : 2 : 1; (b) 78