PSLE
At a walkathon, each participant completed either a 2-km route, a 5-km route or a 7-km route. ¹₃ of the participants completed the 2-km route, ³₁₀ of the participants completed the 5-km route and the rest completed the 7-km route. For every 1 km a participant walked, $6 was donated to charity. A total of $13632 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 7-km route?
2. What is the total number of participants at the walkathon?

(a)
Fraction of the participants who completed 7-km route
= 1 - ¹₃ - ³₁₀
= 1 - ¹⁰₃₀ - ⁹₃₀
= 1 - ¹⁹₃₀
= ¹¹₃₀

Ratio of participants who completed the different routes
2 km : 5 km : 7 km
10 : 9 : 11

(b)
For every 1 km a participant walked, $6 was donated to charity.

Total distance covered by the participants
= 13632 ÷ 6
= 2272 km

	2-km	5-km	7-km	Total
Number	10 u	9 u	11 u	30 u
Value	2	5	7
Total value	20 u	45 u	77 u

Total distance that the participants covered
= 2 x 10 u + 5 x 9 u + 7 x 11 u
= 20 u + 45 u + 77 u
= 142 u

142 u = 2272

1 u = 2272 ÷ 142 = 16

Total number of participants
= 10 u + 9 u + 11 u
= 30 u
= 30 x 16
= 480

Answer(s): (a) 10 : 9 : 11; (b) 480