Question

One car model costs $12,000 & costs and average of $.10 to maintain. Another car model costs $14,000 & costs ab average of $.08 to maintain. If each model is driven the same # of miles, after how many miles would the total cost be the same?

Answer 1

See a solution process below:

Explanation:

Let's call the number of miles driven we are looking for `m`.

The the total cost of ownership for the first car model is:

`12000 + 0.1m`

The the total cost of ownership for the second car model is:

`14000 + 0.08m`

We can equate these two expressions and solve for `m` to find after how many miles the total cost of ownership is the same:

`12000 + 0.1m = 14000 + 0.08m`

Next, we can subtract `color(red)(12000)` and `color(blue)(0.08m)` from each side of the equation to isolate the `m` term while keeping the equation balanced:

`-color(red)(12000) + 12000 + 0.1m - color(blue)(0.08m) = -color(red)(12000) + 14000 + 0.08m - color(blue)(0.08m)`

`0 + (0.1 - color(blue)(0.08))m = 2000 + 0`

`0.02m = 2000`

Now, we can divide each side of the equation by `color(red)(0.02)` to solve for `m` while keeping the equation balanced:

`(0.02m)/color(red)(0.02) = 2000/color(red)(0.02)`

`(color(red)(cancel(color(black)(0.02)))m)/cancel(color(red)(0.02)) = 100000`

After 100,000 miles the total cost of ownership of the two cars would be the same.