PSLE At a swimathon, each participant completed either a 1-km route, a 3-km route or a 4-km route.
13 of the participants completed the 1-km route,
12 of the participants completed the 3-km route and the rest completed the 4-km route. For every 1 km a participant swam, $5 was donated to charity. A total of $975 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 4-km route?
- What is the total number of participants at the swimathon?
(a)
Fraction of the participants who completed 4-km route
= 1 -
13 -
12 = 1 -
26 -
36= 1 -
56 =
16 Ratio of participants who completed the different routes
1 km : 3 km : 4 km
2 : 3 : 1
(b)
For every 1 km a participant swam, $5 was donated to charity.
Total distance covered by the participants
= 975 ÷ 5
= 195 km
|
1-km |
3-km |
4-km |
Total |
Number |
2 u |
3 u |
1 u |
6 u |
Value |
1 |
3 |
4 |
|
Total value |
2 u |
9 u |
4 u |
|
Total distance that the participants covered
= 1 x 2 u + 3 x 3 u + 4 x 1 u
= 2 u + 9 u + 4 u
= 15 u
15 u = 195
1 u = 195 ÷ 15 = 13
Total number of participants
= 2 u + 3 u + 1 u
= 6 u
= 6 x 13
= 78
Answer(s): (a) 2 : 3 : 1; (b) 78