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?

1 Answer
smendyka
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 + 0.1m#

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.

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