Can somehow help justify if my solutions to the problem below is correct and guide me on (b)?

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2 Answers
Oct 19, 2016

Answer:

The customer must travel #6 2/3# Km to reduce average cost at #80#cents/kilometer.

Explanation:

b) let x be the asked kilometer for average cost at 80 cents per kilometer. Then #x*0.80 = 2+(0.50*x) or 0.80x-0.50x=2 or0.30x=2 or x=2/3*10 =20/3=6 2/3 km#[Ans]

Oct 19, 2016

Answer:

For a distance of #6 2/3# km the average cost will be #80c#

Explanation:

#x# is the number of Km travelled.

The total cost of travelling #x# km is calculated as:

#50c" per km" + $2" "larr 50c = $0.50#

#darr" "darr " "darr#

#0.5xx ""x" "+2 = 0.5x+2#

To find the average cost per Km:
divide the total cost by the number of Km travelled.

Ave cost = #f(x) = (0.5x+2)/x#

The average cost for #x# km should be #80c rarr $0.8#

#(0.5x+2)/x = 0.8" "larr xx x#

#0.5x +2 = 0.8x" "larr# move x-terms to the right

#2 = 0.8x-0.5x#

#2 = 0.3x" "larr# divide by 0.3

#2/0.3 = x#

#20/3 = x#

#x = 6 2/3#

For a distance of #6 2/3# km the average cost will be #80c#