PSLE At a swimathon, each participant completed either a 1-km route, a 4-km route or a 5-km route.
23 of the participants completed the 1-km route,
310 of the participants completed the 4-km route and the rest completed the 5-km route. For every 1 km a participant swam, $7 was donated to charity. A total of $6405 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 swimathon?
(a)
Fraction of the participants who completed 5-km route
= 1 -
23 -
310 = 1 -
2030 -
930= 1 -
2930 =
130 Ratio of participants who completed the different routes
1 km : 4 km : 5 km
20 : 9 : 1
(b)
For every 1 km a participant swam, $7 was donated to charity.
Total distance covered by the participants
= 6405 ÷ 7
= 915 km
|
1-km |
4-km |
5-km |
Total |
Number |
20 u |
9 u |
1 u |
30 u |
Value |
1 |
4 |
5 |
|
Total value |
20 u |
36 u |
5 u |
|
Total distance that the participants covered
= 1 x 20 u + 4 x 9 u + 5 x 1 u
= 20 u + 36 u + 5 u
= 61 u
61 u = 915
1 u = 915 ÷ 61 = 15
Total number of participants
= 20 u + 9 u + 1 u
= 30 u
= 30 x 15
= 450
Answer(s): (a) 20 : 9 : 1; (b) 450