Question

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

Answer 1

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]

Answer 2

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`