Final answer:
The two car rental plans cost the same when John drives 250 miles. At that mileage, both plans result in a cost of $81.
Step-by-step explanation:
To find the amount of driving for which the two car rental plans cost the same, we can set up an equation where the total cost of the first plan equals the total cost of the second plan. Let x represent the number of miles driven.
The equation for the first plan is: C1 = 51 + 0.12x, where 51 is the initial fee and 0.12x is the cost per mile.
The equation for the second plan is: C2 = 46 + 0.14x, where 46 is the initial fee and 0.14x is the cost per mile.
To find the number of miles x at which C1 = C2, we set the two equations equal to each other: 51 + 0.12x = 46 + 0.14x.
Solving for x:
Subtract 0.12x from both sides: 51 = 46 + 0.02x
Subtract 46 from both sides: 5 = 0.02x
Divide both sides by 0.02 to find x: x = 250
The two plans cost the same when John drives 250 miles. To find the cost when the two plans are the same, we substitute x into either C1 or C2:
C1 = 51 + 0.12(250) = 51 + 30 = $81
C2 = 46 + 0.14(250) = 46 + 35 = $81
Therefore, both plans cost $81 when John drives 250 miles.