Question

12 At a walkathon, each participant completed either a 3-km route, a 5-km route or an 8-km route. - of the participants completed the 3-km route, as of the 20 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 charity. 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? complete

Answer 1

Answer: a) 5:9:6, b) 380

Explanation:

Let the number of participant be 'x'.

Let the number of participant of 3-km route be
`(x)/(4)`

Let the number of participants of 5-km route be
`(9x)/(20)`

Let the number of participants of 8-km route be

`x-(x)/(4)-(9x)/(20)=(20x-5x-9x)/(20)=(6x)/(20)=(3x)/(10)`

According to question, we get that

`4(3* (x)/(4)+5* (9x)/(20)+8* (3x)/(10))=8208\\\\(3x)/(4)+(9x)/(4)+(24x)/(10)=2052\\\\(15x+45x+48x)/(20)=2052\\\\108x=2052* 20=41040\\\\x=(41040)/(108)\\\\x=380`

Therefore, the number of participants is 380.

Number of participants of 3 km route
`(380)/(4)=95`

Number of participants of 5 km route
`(380* 9)/(20)=171`

Number of participants of 8 km route
`(380* 3)/(10)=114`

Ratio of the number of participants completed 3 km to 5 km to 8 km is given by

95:171:114

=5:9:6

Hence, a) 5:9:6, b) 380