PSLE At a swimathon, each participant completed either a 3-km route, a 5-km route or a 8-km route.
16 of the participants completed the 3-km route,
59 of the participants completed the 5-km route and the rest completed the 8-km route. For every 1 km a participant swam, $8 was donated to charity. A total of $8712 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 8-km route?
- What is the total number of participants at the swimathon?
(a)
Fraction of the participants who completed 8-km route
= 1 -
16 -
59 = 1 -
318 -
1018= 1 -
1318 =
518 Ratio of participants who completed the different routes
3 km : 5 km : 8 km
3 : 10 : 5
(b)
For every 1 km a participant swam, $8 was donated to charity.
Total distance covered by the participants
= 8712 ÷ 8
= 1089 km
|
3-km |
5-km |
8-km |
Total |
Number |
3 u |
10 u |
5 u |
18 u |
Value |
3 |
5 |
8 |
|
Total value |
9 u |
50 u |
40 u |
|
Total distance that the participants covered
= 3 x 3 u + 5 x 10 u + 8 x 5 u
= 9 u + 50 u + 40 u
= 99 u
99 u = 1089
1 u = 1089 ÷ 99 = 11
Total number of participants
= 3 u + 10 u + 5 u
= 18 u
= 18 x 11
= 198
Answer(s): (a) 3 : 10 : 5; (b) 198