PSLE At a swimathon, each participant completed either a 3-km route, a 4-km route or a 5-km route.
14 of the participants completed the 3-km route,
58 of the participants completed the 4-km route and the rest completed the 5-km route. For every 1 km a participant swam, $9 was donated to charity. A total of $3906 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 5-km route?
- What is the total number of participants at the swimathon?
(a)
Fraction of the participants who completed 5-km route
= 1 -
14 -
58 = 1 -
28 -
58= 1 -
78 =
18 Ratio of participants who completed the different routes
3 km : 4 km : 5 km
2 : 5 : 1
(b)
For every 1 km a participant swam, $9 was donated to charity.
Total distance covered by the participants
= 3906 ÷ 9
= 434 km
|
3-km |
4-km |
5-km |
Total |
Number |
2 u |
5 u |
1 u |
8 u |
Value |
3 |
4 |
5 |
|
Total value |
6 u |
20 u |
5 u |
|
Total distance that the participants covered
= 3 x 2 u + 4 x 5 u + 5 x 1 u
= 6 u + 20 u + 5 u
= 31 u
31 u = 434
1 u = 434 ÷ 31 = 14
Total number of participants
= 2 u + 5 u + 1 u
= 8 u
= 8 x 14
= 112
Answer(s): (a) 2 : 5 : 1; (b) 112