College Algebra: New Car Word Problem

Question

You are planning to purchase a new car and have narrowed down your search to two models:

2016 Toyota Prius costs 26800 and gets an average of 50 miles per gallon

2016 Toyota Corolla costs 17900 and gets an average of 32 miles per gallon

 

In either case, the dealer has offered 0% financing, and you can afford the monthly payments for either car. Assume that all costs of ownership are the same (taxes, insurance, maintenance, etc.) If gas costs 2.40 per gallon, how many miles would you have to drive for the total cost (purchase price and fuel used) of the two cars to be equal?

Answer 1

So, Er, let's say I drove 800 miles. The Prius costs (800/50)(2.40) = 38.40. The Corolla costs (800/32)(2.40) = 60

 

Let's call each mile m...

 

26800 + 2.4(m/50) = 17900 + 2.4(m/32)

26800 + 2.4m/50 = 17900 + 2.4m/32

26800 + .048m = 17900 + .075m

.027m = 8900

m = 329,629.63

 

That's a lot of miles!