# 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?

Jun 6, 2017

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:

$12000 + 0.1 m$

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

$14000 + 0.08 m$

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

$12000 + 0.1 m = 14000 + 0.08 m$

Next, we can subtract $\textcolor{red}{12000}$ and $\textcolor{b l u e}{0.08 m}$ from each side of the equation to isolate the $m$ term while keeping the equation balanced:

$- \textcolor{red}{12000} + 12000 + 0.1 m - \textcolor{b l u e}{0.08 m} = - \textcolor{red}{12000} + 14000 + 0.08 m - \textcolor{b l u e}{0.08 m}$

$0 + \left(0.1 - \textcolor{b l u e}{0.08}\right) m = 2000 + 0$

$0.02 m = 2000$

Now, we can divide each side of the equation by $\textcolor{red}{0.02}$ to solve for $m$ while keeping the equation balanced:

$\frac{0.02 m}{\textcolor{red}{0.02}} = \frac{2000}{\textcolor{red}{0.02}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{0.02}}} m}{\cancel{\textcolor{red}{0.02}}} = 100000$

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