PSLE At a swimathon, each participant completed either a 1-km route, a 2-km route or a 5-km route.
12 of the participants completed the 1-km route,
38 of the participants completed the 2-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 $1365 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 2-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 -
12 -
38 = 1 -
48 -
38= 1 -
78 =
18 Ratio of participants who completed the different routes
1 km : 2 km : 5 km
4 : 3 : 1
(b)
For every 1 km a participant swam, $7 was donated to charity.
Total distance covered by the participants
= 1365 ÷ 7
= 195 km
|
1-km |
2-km |
5-km |
Total |
Number |
4 u |
3 u |
1 u |
8 u |
Value |
1 |
2 |
5 |
|
Total value |
4 u |
6 u |
5 u |
|
Total distance that the participants covered
= 1 x 4 u + 2 x 3 u + 5 x 1 u
= 4 u + 6 u + 5 u
= 15 u
15 u = 195
1 u = 195 ÷ 15 = 13
Total number of participants
= 4 u + 3 u + 1 u
= 8 u
= 8 x 13
= 104
Answer(s): (a) 4 : 3 : 1; (b) 104