Gas prices have varied over the last month. You have notated each time you filled up your car and the price of gas at the time you filled up. You want to calculate the average price for a gallon of gas. You first bought 9.4 gallons for \( \$ 3.69 \) per gallon, then you bought 9.8 gallons for \( \$ 3.49 \) per gallon, then 9.6 gallons for \( \$ 3.09 \) per gallon, and finally 9.5 gallons for \( \$ 2.99 \) per gallon. Calculate the weighted average in dollars per gallon. Round to the nearest cent. \( \$ \)

To calculate the weighted average price per gallon of gas, we need to multiply the price per gallon by the number of gallons purchased for each transaction, sum these products, and then divide by the total number of gallons purchased. Let's calculate the weighted average price per gallon of gas step by step: 1. Calculate the total cost for each transaction: - For the first transaction: \( 9.4 \times \$3.69 \) - For the second transaction: \( 9.8 \times \$3.49 \) - For the third transaction: \( 9.6 \times \$3.09 \) - For the fourth transaction: \( 9.5 \times \$2.99 \) 2. Sum the total costs from all transactions. 3. Calculate the total number of gallons purchased. 4. Divide the total cost by the total number of gallons to find the weighted average price per gallon. Let's perform these calculations. Calculate the value by following steps: - step0: Calculate: \(9.4\times 3.69\) - step1: Multiply the numbers: \(34.686\) The total cost for the first transaction is $34.686. Now, let's calculate the total cost for the second transaction. Calculate the value by following steps: - step0: Calculate: \(9.8\times 3.49\) - step1: Multiply the numbers: \(34.202\) The total cost for the second transaction is $34.202. Next, let's calculate the total cost for the third transaction. Calculate the value by following steps: - step0: Calculate: \(9.6\times 3.09\) - step1: Multiply the numbers: \(29.664\) The total cost for the third transaction is $29.664. Now, let's calculate the total cost for the fourth transaction. Calculate the value by following steps: - step0: Calculate: \(9.5\times 2.99\) - step1: Multiply the numbers: \(28.405\) The total cost for the fourth transaction is $28.405. Now, let's sum up the total costs from all transactions to find the total cost. Calculate the value by following steps: - step0: Calculate: \(34.686+34.202+29.664+28.405\) - step1: Add the numbers: \(126.957\) The total cost from all transactions is $126.957. Next, let's calculate the total number of gallons purchased. Calculate the value by following steps: - step0: Calculate: \(9.4+9.8+9.6+9.5\) - step1: Add the numbers: \(38.3\) The total number of gallons purchased is 38.3 gallons. Finally, let's calculate the weighted average price per gallon by dividing the total cost by the total number of gallons. Calculate the value by following steps: - step0: Calculate: \(\frac{126.957}{38.3}\) - step1: Convert the expressions: \(\frac{\frac{126957}{1000}}{\frac{383}{10}}\) - step2: Multiply by the reciprocal: \(\frac{126957}{1000}\times \frac{10}{383}\) - step3: Reduce the numbers: \(\frac{126957}{100}\times \frac{1}{383}\) - step4: Multiply the fractions: \(\frac{126957}{100\times 383}\) - step5: Multiply: \(\frac{126957}{38300}\) The weighted average price per gallon of gas is approximately $3.31.