Solving a decimal word problem using a two-step linear inequality Heather is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges \( \$ 110 \) and allows unlimited mileage. Company B has an initial fee of \( \$ 65 \) and charges an additional \( \$ 0.60 \) for every mile driven. For what mileages will Company A charge less than Company B? Use \( m \) for the number of miles driven, and solve your inequality for \( m \). Und

To find out when Company A is cheaper than Company B, we set up the inequality: \[ 110 < 65 + 0.60m. \] To solve this, first subtract 65 from both sides: \[ 110 - 65 < 0.60m \] which simplifies to: \[ 45 < 0.60m. \] Now, divide both sides by 0.60: \[ m > \frac{45}{0.60}. \] Calculating that gives: \[ m > 75. \] So, Company A is the cheaper option when Heather drives more than 75 miles. If you drive 75 miles, Company A would cost $110, while Company B would charge $65 plus \( 0.60 \times 75 = \$45 \), totaling up to $110. However, as soon as she drives even 76 miles, Company B would start to cost more, racking up to \$65 + \$45.60, resulting in $110.60! So, anything beyond that and Company B is more expensive! Remember, it's always wise to consider how far you plan to go before making those rental decisions. When tackling decimal word problems, it's essential to double-check your calculations; common mistakes can include misplacing the decimal or incorrect addition/subtraction with the fees. Make sure to clearly identify your variables and write your equations step by step. Additionally, it can be helpful to plug in values to ensure you’ve correctly interpreted the inequality, as this can illustrate your answer vividly and verify your work!