I am buying a used vehicle. I want an equation that will allow me to compare two vehicle's value that are identical in every way except price and mileage. For example:

Car A: $20395 cost and 83400 miles

Car B: $17090 cost and 10500 miles

Car C: $24000 cost and 39000 miles

Miles: lower miles = good

Cost: higher cost = bad

What is a ratio/equation that can produce a number to compare these two variables across vehicles?


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  • 2
    $\begingroup$ You don't need an equation. The cheapest car is the car with fewest miles. What's the problem? $\endgroup$ – Dog_69 Mar 16 at 17:40
  • $\begingroup$ You may think of something like: $c + k \times m$, where $c$ is the cost of the car, $m$ is the number of miles it travelled so far and $k$ is how much you expect to spend on maintenance of your car due to the $m$ miles it already travelled. $\endgroup$ – Ertxiem Mar 16 at 18:19
  • $\begingroup$ Dog_69 That's not always true. So which is the best value per mile car out of these: Car A $16000 at 83379 mi; Car B $24500 at 38341 mi; Car C $19400 at 76,707 miles? $\endgroup$ – Frank Mar 16 at 18:57
  • $\begingroup$ Ertxiem, I don't want to factor maintenance cost. I just want to compare across these two variables. $\endgroup$ – Frank Mar 16 at 18:59

Decide on a number of miles that represents a wore-out car and call that number as w.


(miles / w) * price = index value .

But large differences in price become relatively insignificant at small mileages.

New edit:

Or instead

index value = (w - miles) / price .

That's actually miles-remaining-per-dollar. But that doesn't hold for negative values.

  • $\begingroup$ @S Spring: So the higher the index number, the worse deal/value the vehicle is, correct. I want the vehicle with the lowest index value? Thank you so much. Can't tell you how many math majors and teachers I've given this problem and none of them have come up with an equation for an index. $\endgroup$ – Frank Mar 16 at 23:20

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