\begin{tabular}{l} Use for questions 22 and 23 Darius filled up his gas tank with 24 gallons of gas. For each mile that he \\ drives, he uses 0.06 gallons of gas. \\ \( \begin{array}{l}\text { 22. Which formula represents the number of } \\ \text { gallons of gas left affer driving } n \text { miles? }\end{array} \) \\ \hline \( \begin{array}{l}\text { 23. How many gallons of gas are left in the tank } \\ \text { after driving } 240 \text { miles? }\end{array} \) \\ \( \begin{array}{l}\text { A. } a_{n}=-0.06 n+23.94 \\ \text { B. } a_{n}=-0.06 n+24 \\ \text { C. } a_{n}=-0.06 n+24.06 \\ \text { D. } a_{n}=0.06 n-24\end{array} \) \\ \hline\end{tabular}

To solve the problem, we will break it down into two parts as indicated by the questions. ### Question 22: Formula for Gallons of Gas Left 1. **Identify the known values:** - Initial gallons of gas: \( 24 \) gallons - Gallons used per mile: \( 0.06 \) gallons/mile - Distance driven: \( n \) miles 2. **Determine the gallons of gas used after driving \( n \) miles:** - The total gallons used after driving \( n \) miles can be calculated as: \[ \text{Gallons used} = 0.06n \] 3. **Calculate the gallons of gas left:** - The gallons of gas left after driving \( n \) miles is given by: \[ \text{Gallons left} = \text{Initial gallons} - \text{Gallons used} \] - Substituting the known values: \[ a_n = 24 - 0.06n \] 4. **Rearranging the equation:** - This can be rewritten as: \[ a_n = -0.06n + 24 \] 5. **Select the correct formula:** - From the options provided, the correct formula is: \[ \text{B. } a_n = -0.06n + 24 \] ### Question 23: Gallons of Gas Left After Driving 240 Miles 1. **Use the formula derived in Question 22:** - We will substitute \( n = 240 \) into the formula: \[ a_n = -0.06(240) + 24 \] 2. **Calculate the gallons used:** - First, calculate \( 0.06 \times 240 \): \[ 0.06 \times 240 = 14.4 \] 3. **Calculate the gallons left:** - Now substitute this value back into the formula: \[ a_n = -14.4 + 24 \] - Simplifying this gives: \[ a_n = 9.6 \] ### Final Answers: - **22.** The formula representing the number of gallons of gas left after driving \( n \) miles is: \[ a_n = -0.06n + 24 \] - **23.** The number of gallons of gas left in the tank after driving \( 240 \) miles is: \[ 9.6 \text{ gallons} \]