PSLE At a swimathon, each participant completed either a 3-km route, a 5-km route or a 7-km route.
16 of the participants completed the 3-km route,
12 of the participants completed the 5-km route and the rest completed the 7-km route. For every 1 km a participant swam, $5 was donated to charity. A total of $1920 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 7-km route?
- What is the total number of participants at the swimathon?
(a)
Fraction of the participants who completed 7-km route
= 1 -
16 -
12 = 1 -
16 -
36= 1 -
46 =
26 Ratio of participants who completed the different routes
3 km : 5 km : 7 km
1 : 3 : 2
(b)
For every 1 km a participant swam, $5 was donated to charity.
Total distance covered by the participants
= 1920 ÷ 5
= 384 km
|
3-km |
5-km |
7-km |
Total |
Number |
1 u |
3 u |
2 u |
6 u |
Value |
3 |
5 |
7 |
|
Total value |
3 u |
15 u |
14 u |
|
Total distance that the participants covered
= 3 x 1 u + 5 x 3 u + 7 x 2 u
= 3 u + 15 u + 14 u
= 32 u
32 u = 384
1 u = 384 ÷ 32 = 12
Total number of participants
= 1 u + 3 u + 2 u
= 6 u
= 6 x 12
= 72
Answer(s): (a) 1 : 3 : 2; (b) 72