Final answer:
To determine when the rental costs of two different cars are equal, we set up an equation based on their respective rental fees and per-mile charges and solve for the number of miles. Upon doing the calculation, it turns out that the costs are equal after driving 350 miles, which doesn't match any of the options given in the question.
Step-by-step explanation:
To find out when the cost of renting two different cars will be the same based on their initial cost and per-mile charge, we can set up an equation where both cost functions are equal.
Let x be the number of miles driven. The cost function for the first car is C1 = 46 + 0.15x, and for the second car it's C2 = 53 + 0.13x. To find out when the costs are the same, we can solve for x in the equation 46 + 0.15x = 53 + 0.13x.
Simplify by subtracting 0.13x from both sides: 0.02x = 53 - 46,
Further simplify to get: 0.02x = 7.
Divide both sides by 0.02 to solve for x: x = 7 / 0.02,
Which simplifies to: x = 350.
Therefore, the two cars will cost the same after driving 350 miles, which is not one of the answer choices provided.