PSLE At a swimathon, each participant completed either a 1-km route, a 4-km route or a 7-km route.
23 of the participants completed the 1-km route,
14 of the participants completed the 4-km route and the rest completed the 7-km route. For every 1 km a participant swam, $8 was donated to charity. A total of $4320 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 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 -
23 -
14 = 1 -
812 -
312= 1 -
1112 =
112 Ratio of participants who completed the different routes
1 km : 4 km : 7 km
8 : 3 : 1
(b)
For every 1 km a participant swam, $8 was donated to charity.
Total distance covered by the participants
= 4320 ÷ 8
= 540 km
|
1-km |
4-km |
7-km |
Total |
Number |
8 u |
3 u |
1 u |
12 u |
Value |
1 |
4 |
7 |
|
Total value |
8 u |
12 u |
7 u |
|
Total distance that the participants covered
= 1 x 8 u + 4 x 3 u + 7 x 1 u
= 8 u + 12 u + 7 u
= 27 u
27 u = 540
1 u = 540 ÷ 27 = 20
Total number of participants
= 8 u + 3 u + 1 u
= 12 u
= 12 x 20
= 240
Answer(s): (a) 8 : 3 : 1; (b) 240