# Question

At a walkathon, each participant competed either a 3-km route, a 5-km route or an 8-km route. 1/4 of the participants completed the 3-km route, 9/20 of the participants completed the 5-km route and the rest completed the 8-km route.

For every 1 km a participant walked, \$4 was donated to charit. A total of \$8208 was donated to charity.

a) 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 8-km route?

b) What is the total number of participants at the walkathon?

This is a Quantity Each Product question.

1. LCM

1/4  = 5/20

9/20

 Quantity Each Product 3km 5u 3 15u 5km 9u 5 45u 8km 6u 8 48u Total 20u 108u

a)

5 : 9 : 6

b)

108u  = 8208

1u = 8208 ÷ 108 = 76

20u = 76 × 20 = 1520

😊

For part B, take note that it’s for every km, \$4 is donated. Hence should divide 8208 by 4 before finding 1u

108u = 8208/4

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(a)
total participants : 20 units
3-km : (1/4) x 20 = 5 units
5-km : 9 units
8-km : 20 – 5 – 9 = 6 units
5 : 9 : 6

(b)
3 x 5 x 4 = 60
5 x 9 x 4 = 180
8 x 6 x 4 = 192
60 + 180 + 192 = 432 (groups/sets)
8208/432 = 19
20 x 19 = 380

Ans : (a) 5 : 9 : 6; (b) 380 participants.

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