Solving a decimal word problem using a linear Inequality with the variabl... Alan is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges an initial fee of \( \$ 65 \) and an additional 50 cents for every mile driven. Company B charges an initial fee of \( \$ 60 \) and an additional 60 cents for every mile driven. For what mileages will Company A charge no more than Company B? Write your answer as an inequality, using \( m \) for the number of miles driven.

To determine when Company A charges no more than Company B, we can set up the costs based on the given information. Let \( m \) be the number of miles driven. The cost for Company A can be expressed as: \[ \text{Cost of Company A} = 65 + 0.5m \] The cost for Company B can be expressed as: \[ \text{Cost of Company B} = 60 + 0.6m \] We want to find when Company A's cost is less than or equal to Company B's cost: \[ 65 + 0.5m \leq 60 + 0.6m \] Now, we can solve this inequality: 1. Subtract \( 0.5m \) from both sides: \[ 65 \leq 60 + 0.1m \] 2. Subtract 60 from both sides: \[ 5 \leq 0.1m \] 3. Finally, divide by 0.1: \[ m \geq 50 \] So, Company A will charge no more than Company B when the mileage \( m \) is 50 miles or more. In summary, the inequality representing the situation is: \[ m \geq 50 \] Now, onto some interesting tidbits! Ever wondered how truck rental pricing has evolved? In the past, truck rentals were almost entirely based on flat rates, which only covered a certain mileage limit. As companies began to compete in the market, they started incorporating mileage charges to cater to different customers' needs, leading to the pricing models we see today. It’s a fascinating blend of economics and consumer behavior! For anyone considering renting a truck, it’s crucial to do a little math beforehand! A common mistake is failing to account for all the extra fees that can sneak in, like insurance or taxes. When comparing companies, always calculate the total cost based on your expected mileage to avoid any unexpected charges at checkout. Doing your homework pays off in more ways than one!