PSLE At a swimathon, each participant completed either a 2-km route, a 5-km route or a 6-km route.
23 of the participants completed the 2-km route,
310 of the participants completed the 5-km route and the rest completed the 6-km route. For every 1 km a participant swam, $8 was donated to charity. A total of $14560 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 6-km route?
- What is the total number of participants at the swimathon?
(a)
Fraction of the participants who completed 6-km route
= 1 -
23 -
310 = 1 -
2030 -
930= 1 -
2930 =
130 Ratio of participants who completed the different routes
2 km : 5 km : 6 km
20 : 9 : 1
(b)
For every 1 km a participant swam, $8 was donated to charity.
Total distance covered by the participants
= 14560 ÷ 8
= 1820 km
|
2-km |
5-km |
6-km |
Total |
Number |
20 u |
9 u |
1 u |
30 u |
Value |
2 |
5 |
6 |
|
Total value |
40 u |
45 u |
6 u |
|
Total distance that the participants covered
= 2 x 20 u + 5 x 9 u + 6 x 1 u
= 40 u + 45 u + 6 u
= 91 u
91 u = 1820
1 u = 1820 ÷ 91 = 20
Total number of participants
= 20 u + 9 u + 1 u
= 30 u
= 30 x 20
= 600
Answer(s): (a) 20 : 9 : 1; (b) 600