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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

Respuesta :

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

Step-by-step explanation:

Let the number of participant be 'x'.

Let the number of participant of 3-km route be [tex]\dfrac{x}{4}[/tex]

Let the number of participants of 5-km route be [tex]\dfrac{9x}{20}[/tex]

Let the number of participants of 8-km route be

[tex]x-\dfrac{x}{4}-\dfrac{9x}{20}=\dfrac{20x-5x-9x}{20}=\dfrac{6x}{20}=\dfrac{3x}{10}[/tex]

According to question, we get that

[tex]4(3\times \dfrac{x}{4}+5\times \dfrac{9x}{20}+8\times \dfrac{3x}{10})=8208\\\\\dfrac{3x}{4}+\dfrac{9x}{4}+\dfrac{24x}{10}=2052\\\\\dfrac{15x+45x+48x}{20}=2052\\\\108x=2052\times 20=41040\\\\x=\dfrac{41040}{108}\\\\x=380[/tex]

Therefore, the number of participants is 380.

Number of participants of 3 km route [tex]\dfrac{380}{4}=95[/tex]

Number of participants of 5 km route  [tex]\dfrac{380\times 9}{20}=171[/tex]

Number of participants of 8 km route  [tex]\dfrac{380\times 3}{10}=114[/tex]

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

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