PSLE
At a swimathon, each participant completed either a 1-km route, a 4-km route or a 5-km route. ¹₃ of the participants completed the 1-km route, ¹₂ of the participants completed the 4-km route and the rest completed the 5-km route. For every 1 km a participant swam, $10 was donated to charity. A total of $3230 was donated to charity.

1. 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?
2. What is the total number of participants at the swimathon?

(a)
Fraction of the participants who completed 5-km route
= 1 - ¹₃ - ¹₂
= 1 - ²₆ - ³₆
= 1 - ⁵₆
= ¹₆

Ratio of participants who completed the different routes
1 km : 4 km : 5 km
2 : 3 : 1

(b)
For every 1 km a participant swam, $10 was donated to charity.

Total distance covered by the participants
= 3230 ÷ 10
= 323 km

	1-km	4-km	5-km	Total
Number	2 u	3 u	1 u	6 u
Value	1	4	5
Total value	2 u	12 u	5 u

Total distance that the participants covered
= 1 x 2 u + 4 x 3 u + 5 x 1 u
= 2 u + 12 u + 5 u
= 19 u

19 u = 323

1 u = 323 ÷ 19 = 17

Total number of participants
= 2 u + 3 u + 1 u
= 6 u
= 6 x 17
= 102

Answer(s): (a) 2 : 3 : 1; (b) 102