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?

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

Step-by-step 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