PSLE
At a swimathon, each participant completed either a 2-km route, a 5-km route or a 6-km route. ¹₃ of the participants completed the 2-km route, ⁵₈ of the participants completed the 5-km route and the rest completed the 6-km route. For every 1 km a participant swam, $5 was donated to charity. A total of $5820 was donated to charity.

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

(a)
Fraction of the participants who completed 6-km route
= 1 - ¹₃ - ⁵₈
= 1 - ⁸₂₄ - ¹⁵₂₄
= 1 - ²³₂₄
= ¹₂₄

Ratio of participants who completed the different routes
2 km : 5 km : 6 km
8 : 15 : 1

(b)
For every 1 km a participant swam, $5 was donated to charity.

Total distance covered by the participants
= 5820 ÷ 5
= 1164 km

	2-km	5-km	6-km	Total
Number	8 u	15 u	1 u	24 u
Value	2	5	6
Total value	16 u	75 u	6 u

Total distance that the participants covered
= 2 x 8 u + 5 x 15 u + 6 x 1 u
= 16 u + 75 u + 6 u
= 97 u

97 u = 1164

1 u = 1164 ÷ 97 = 12

Total number of participants
= 8 u + 15 u + 1 u
= 24 u
= 24 x 12
= 288

Answer(s): (a) 8 : 15 : 1; (b) 288