PSLE At a walkathon, each participant completed either a 1-km route, a 4-km route or a 5-km route.
14 of the participants completed the 1-km route,
23 of the participants completed the 4-km route and the rest completed the 5-km route. For every 1 km a participant walked, $8 was donated to charity. A total of $5760 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 5-km route?
- What is the total number of participants at the walkathon?
(a)
Fraction of the participants who completed 5-km route
= 1 -
14 -
23 = 1 -
312 -
812= 1 -
1112 =
112 Ratio of participants who completed the different routes
1 km : 4 km : 5 km
3 : 8 : 1
(b)
For every 1 km a participant walked, $8 was donated to charity.
Total distance covered by the participants
= 5760 ÷ 8
= 720 km
|
1-km |
4-km |
5-km |
Total |
Number |
3 u |
8 u |
1 u |
12 u |
Value |
1 |
4 |
5 |
|
Total value |
3 u |
32 u |
5 u |
|
Total distance that the participants covered
= 1 x 3 u + 4 x 8 u + 5 x 1 u
= 3 u + 32 u + 5 u
= 40 u
40 u = 720
1 u = 720 ÷ 40 = 18
Total number of participants
= 3 u + 8 u + 1 u
= 12 u
= 12 x 18
= 216
Answer(s): (a) 3 : 8 : 1; (b) 216