Final answer:
After 109,300 miles, the cost of the gas-only SUV, which has an initial cost of $26,445 and an average maintenance cost of $0.18 per mile, will exceed the cost of the hybrid SUV, which has an initial cost of $31,910 and an average maintenance cost of $0.13 per mile.
Step-by-step explanation:
To calculate after how many miles the cost of the gas-only SUV will exceed the cost of the hybrid model, we need to set up an equation where the total costs of both vehicles are equal and then solve for the number of miles.
Let's define the following variables:
-
- Cg = Total cost of gas-only SUV
-
- Ch = Total cost of the hybrid SUV
-
- m = Number of miles driven
The initial cost of the gas-only SUV is $26,445 and its maintenance cost per mile is $0.18. Thus, its total cost Cg can be expressed as:
Cg = $26,445 + $0.18m
The initial cost of the hybrid SUV is $31,910 and its maintenance cost per mile is $0.13. Thus, its total cost Ch can be expressed as:
Ch = $31,910 + $0.13m
We set Cg equal to Ch to find the point where both costs are the same:
$26,445 + $0.18m = $31,910 + $0.13m
To solve for m, subtract $26,445 and $0.13m from both sides:
$0.05m = $5,465
Divide both sides by $0.05 to isolate m:
m = $5,465 / $0.05
m = 109,300 miles
Therefore, after 109,300 miles, the cost of the gas-only SUV will exceed the cost of the hybrid SUV.