PSLE
At a walkathon, each participant completed either a 3-km route, a 5-km route or a 7-km route. ²₅ of the participants completed the 3-km route, ¹₂ 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 $4752 was donated to charity.

1. What is the ratio of the number of participants who completed the 3-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 - ²₅ - ¹₂
= 1 - ⁴₁₀ - ⁵₁₀
= 1 - ⁹₁₀
= ¹₁₀

Ratio of participants who completed the different routes
3 km : 5 km : 7 km
4 : 5 : 1

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

Total distance covered by the participants
= 4752 ÷ 6
= 792 km

	3-km	5-km	7-km	Total
Number	4 u	5 u	1 u	10 u
Value	3	5	7
Total value	12 u	25 u	7 u

Total distance that the participants covered
= 3 x 4 u + 5 x 5 u + 7 x 1 u
= 12 u + 25 u + 7 u
= 44 u

44 u = 792

1 u = 792 ÷ 44 = 18

Total number of participants
= 4 u + 5 u + 1 u
= 10 u
= 10 x 18
= 180

Answer(s): (a) 4 : 5 : 1; (b) 180