Question

An SUV costs 27,510 and costs an average of0.18 per mile to maintain. A hybrid model of the SUV costs 33,135 and costs an average of0.13 per mile to maintain. After how many miles will the cost of the gas-only SUV exceed the cost of the hybrid?

Answer 1

The cost of the gas-only SUV will exceed the cost of the hybrid after 112,500 miles, calculated by equating the total costs of both vehicles considering their initial purchase cost and maintenance cost per mile.

Step-by-step explanation:

To determine after how many miles the cost of the gas-only SUV will exceed the cost of the hybrid, we need to set up an equation where the total cost of each vehicle (initial purchase cost plus maintenance costs) becomes equal. Let’s denote the number of miles driven as x.

For the gas-only SUV, the total cost will be the initial cost plus the maintenance cost per mile times the number of miles driven, which is:
$27,510 + $0.18x.

For the hybrid, the total cost is:
$33,135 + $0.13x.

We want to find out when the total cost of the gas-only SUV exceeds that of the hybrid. So we will set the gas-only SUV's total cost greater than the hybrid's total cost:
$27,510 + $0.18x > $33,135 + $0.13x.

Subtracting $0.13x from both sides gives:
$0.05x > $5,625.

Now, divide both sides by $0.05 to solve for x:
x > 112,500 miles.

Therefore, after 112,500 miles, the total cost for the gas-only SUV will exceed that of the hybrid.