If you rent a car from Risky Rental for $40 per day plus $0.08 per mile, how many miles make it cheaper than Comfy Car Rental at $35 per day plus $0.13 per mile?

To determine how many miles make renting from Risky Rental cheaper than Comfy Car Rental, we first need to set up equations to represent the total costs for both rental companies based on the number of miles driven, denoted as ( x ).

For Risky Rental, the total cost can be expressed as:

[ \text{Cost}_{Risky} = 40 + 0.08x ]

For Comfy Car Rental, the total cost can be expressed as:

[ \text{Cost}_{Comfy} = 35 + 0.13x ]

To find when Risky Rental becomes cheaper, we need to set up the inequality:

[ 40 + 0.08x < 35 + 0.13x ]

Now, we can solve this inequality step by step. First, we can isolate the ( x ) terms on one side by subtracting ( 0.08x ) from both sides:

[ 40 < 35 + 0.05x ]

Next, we subtract 35 from both sides to continue isolating ( x ):

[ 5 < 0.05x ]

Now, divide both sides by ( 0.05 ) to solve