PSLE At a walkathon, each participant completed either a 2-km route, a 5-km route or a 7-km route.
16 of the participants completed the 2-km route,
23 of the participants completed the 5-km route and the rest completed the 7-km route. For every 1 km a participant walked, $6 was donated to charity. A total of $3132 was donated to charity.
- What is the ratio of the number of participants who completed the 2-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 walkathon?
(a)
Fraction of the participants who completed 7-km route
= 1 -
16 -
23 = 1 -
16 -
46= 1 -
56 =
16 Ratio of participants who completed the different routes
2 km : 5 km : 7 km
1 : 4 : 1
(b)
For every 1 km a participant walked, $6 was donated to charity.
Total distance covered by the participants
= 3132 ÷ 6
= 522 km
|
2-km |
5-km |
7-km |
Total |
Number |
1 u |
4 u |
1 u |
6 u |
Value |
2 |
5 |
7 |
|
Total value |
2 u |
20 u |
7 u |
|
Total distance that the participants covered
= 2 x 1 u + 5 x 4 u + 7 x 1 u
= 2 u + 20 u + 7 u
= 29 u
29 u = 522
1 u = 522 ÷ 29 = 18
Total number of participants
= 1 u + 4 u + 1 u
= 6 u
= 6 x 18
= 108
Answer(s): (a) 1 : 4 : 1; (b) 108