Define variables and write a system of equations for each situation. Solve using substitution.

Suppose you are thinking about buying one of two cars. Car A will cost $17,655. Youn can expect to pay an average of $1230 per year for fuel, maintenance, and repairs. Car B will cost about $15,900. Fuel, maintenance, and repairs for it will average about $1425 per year. After how many years are the total costs for the cars the same?

5 answers

From your wording,

17,655 + 1230X = 15,900 + 1425X

Solve for X.

I hope this helps. Thanks for asking.

Bhj677

11 years

No the true answer is 9 years

To solve this problem using substitution, let's define the following variables:

Let's say x represents the number of years for which we want to calculate the total cost of the cars.

Now, let's write the system of equations comparing the total costs for each car:

For Car A:
Total Cost of Car A = Cost of Car A + (Annual Cost of Fuel, Maintenance, and Repairs for Car A * Number of Years)
Total Cost of Car A = $17,655 + ($1,230 * x)

For Car B:
Total Cost of Car B = Cost of Car B + (Annual Cost of Fuel, Maintenance, and Repairs for Car B * Number of Years)
Total Cost of Car B = $15,900 + ($1,425 * x)

To find out after how many years the total costs for the cars are the same, we can set the two equations equal to each other and solve for x:

$17,655 + ($1,230 * x) = $15,900 + ($1,425 * x)

Now, we can solve the equation using substitution:

Subtract $15,900 from both sides:
$17,655 + ($1,230 * x) - $15,900 = $15,900 + ($1,425 * x) - $15,900

Simplify:
$1,755 + ($1,230 * x) = ($1,425 * x)

Subtract ($1,230 * x) from both sides:
$1,755 = ($1,425 * x) - ($1,230 * x)

Simplify:
$1,755 = $195 * x

Divide both sides by $195:
$1,755 / $195 = ($195 * x) / $195

Simplify:
9 = x

So, after 9 years, the total costs for Car A and Car B would be the same.