\( \therefore \) www-awu aleks.com/alekscgi/x/lslexe/1o_u-IgNslkr7j8P3jH-IJiOnPgEsPrkicRI6p56oAVDiQYFU2vvpW5CZFZDIO23Nol4pFtOdLW3rAJOAK3h5sp6be. Unear Equations and Incequathices 15 Solving a decimal word problem using a two-step linear inequality Lena 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 \$82 and allows unlimited mileage. Company B has an initial fee of \$55 and charges an additional \$0.90 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 \( m \). \( \square \) \( <\square \) \( \square \)

To solve the problem, we need to set up an inequality based on the costs of renting the truck from both companies. ### Known Conditions: - **Company A** charges a flat fee of \$82 with unlimited mileage. - **Company B** charges an initial fee of \$55 plus \$0.90 for every mile driven. ### Step 1: Set up the cost equations Let \( m \) represent the number of miles driven. - The cost for Company A: \[ C_A = 82 \] - The cost for Company B: \[ C_B = 55 + 0.90m \] ### Step 2: Set up the inequality We want to find the mileages for which Company A is cheaper than Company B: \[ C_A < C_B \] Substituting the cost equations: \[ 82 < 55 + 0.90m \] ### Step 3: Solve the inequality Now, we will solve the inequality step by step. 1. Subtract 55 from both sides: \[ 82 - 55 < 0.90m \] \[ 27 < 0.90m \] 2. Divide both sides by 0.90: \[ \frac{27}{0.90} < m \] Now, let's calculate \( \frac{27}{0.90} \). ### Step 4: Calculate \( \frac{27}{0.90} \) I will perform the calculation now. Calculate the value by following steps: - step0: Calculate: \(\frac{27}{0.9}\) - step1: Convert the expressions: \(\frac{27}{\frac{9}{10}}\) - step2: Multiply by the reciprocal: \(27\times \frac{10}{9}\) - step3: Reduce the numbers: \(3\times 10\) - step4: Multiply the numbers: \(30\) The calculation gives us: \[ \frac{27}{0.90} = 30 \] ### Step 5: Write the final inequality Thus, we have: \[ 30 < m \] or equivalently, \[ m > 30 \] ### Conclusion Lena should choose Company A if she drives more than 30 miles. Therefore, the solution to the inequality is: \[ m > 30 \]