Question

Mary's car has broken down and it will cost her $1200 to get it fixed—or, for $4500, she can buy a new, more efficient car instead. Her present car uses about $2000 worth of gas per year, while gas for the new car would cost about $1500 per year. After how many years would the total cost of fixing the car equal the total cost of replacing it?

Answer 1

it is less expensive to keep your old car.

Answer 2

Answer: it will take 6.6 years for both costs to be the same.

Explanation:

Let x represent the number of years that it will take for the total cost of fixing the car to equal the total cost of replacing it.

It will cost Mary $1200 to fix her car. Her present car uses about $2000 worth of gas per year, it means that the total cost of fixing the car and using it for x years is

1200 + 2000x

It will cost her $4500 to buy a new car while gas for the new car would cost about $1500 per year. it means that the total cost of buying the car and using it for x years is

4500 + 1500x

Therefore, for the total cost of fixing the car to equal the total cost of replacing it, the number of years would be

1200 + 2000x = 4500 + 1500x

2000x - 1500x = 4500 - 1200

500x = 3300

x = 3300/500

x = 6.6