Questions: Linear Equations and Inequalities Solving a decimal word problem using a linear inequality with the variable... Dan 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 50 and an additional 50 cents for every mile driven. Company B has no initial fee but charges 60 cents for every mile driven. For what mileages will Company A charge more than Company B? Use m for the number of miles driven, and solve your inequality for m.

Solution Steps

To determine for what mileages Company A will charge more than Company B, we need to set up an inequality comparing the total costs from both companies. Let \( m \) be the number of miles driven. The cost for Company A is given by \( 50 + 0.50m \) and the cost for Company B is given by \( 0.60m \). We need to find the values of \( m \) for which the cost of Company A is greater than the cost of Company B.

1. Set up the inequality: \( 50 + 0.50m > 0.60m \).
2. Solve for \( m \) by isolating the variable on one side of the inequality.

We start by comparing the costs of the two companies. The cost for Company A is given by: \[ C_A = 50 + 0.50m \] The cost for Company B is given by: \[ C_B = 0.60m \] We need to find when Company A's cost is greater than Company B's cost: \[ 50 + 0.50m > 0.60m \]

To solve the inequality, we rearrange it: \[ 50 > 0.60m - 0.50m \] This simplifies to: \[ 50 > 0.10m \]

Now, we isolate \( m \) by dividing both sides by \( 0.10 \): \[ m < \frac{50}{0.10} \] Calculating the right side gives: \[ m < 500 \]

Final Answer