Final answer:
To find the number of miles you must drive to have the same cost for each of the car rentals, set up and solve an equation. The answer is 40 miles.
Step-by-step explanation:
To find the number of miles you must drive to have the same cost for each of the car rentals, we need to set up and solve an equation.
a) For the first car rental, the cost is given by the equation: Cost = $20 + $0.50(miles).
b) For the second car rental, the cost is given by the equation: Cost = $30 + $0.25(miles).
To find the number of miles, we can set these two equations equal to each other and solve for miles:
$20 + $0.50(miles) = $30 + $0.25(miles)
Combining like terms, we get: $0.50(miles) - $0.25(miles) = $30 - $20
Simplifying further, we have: $0.25(miles) = $10
Dividing both sides by $0.25, we find that miles = 40.
Therefore, you must drive 40 miles to have the same cost for each of the car rentals.