A car service charges customers a flat fee per ride (which is higher during rush hour traffic) plus charges for each minute and each mile. Suppose that, in a certain metropolitan area during rush hour, the flat fee is \( \$ 5 \), the cost per minute is \( \$ 0.30 \), and the cost per mile is \( \$ 1.20 \). Let \( x \) be the number of minutes and \( y \) the number of miles. At the end of a ride, the driver said that the passenger owed \( \$ 11.30 \) and remarked that the number of minutes was three times the number of miles. Find the number of minutes and the number of miles for this trip. \( 5+0.30 x+1.20 y=11.30 \) (Do not include the \( \$ \) symbol in your answer. Do not simplify. Use integers or decimals for any numbers in the equation.) Complete the equation that represents the relationship between the number of minutes and number of miles. \( \square=0 \) (Do not simplify. Use integers or decimals for any numbers in the equation.)

Given: - Flat fee per ride during rush hour: $5 - Cost per minute: $0.30 - Cost per mile: $1.20 - Total cost for the ride: $11.30 - Relationship between the number of minutes and miles: \( x = 3y \) We can represent the total cost for the ride using the given information: \[ 5 + 0.30x + 1.20y = 11.30 \] Now, we need to find the number of minutes (\( x \)) and the number of miles (\( y \)) for this trip. We can solve the system of equations formed by the total cost equation and the relationship between minutes and miles. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}5+0.3x+1.2y=11.3\\x=3y\end{array}\right.\) - step1: Substitute the value of \(x:\) \(5+0.3\times 3y+1.2y=11.3\) - step2: Simplify: \(5+2.1y=11.3\) - step3: Move the constant to the right side: \(2.1y=11.3-5\) - step4: Subtract the numbers: \(2.1y=6.3\) - step5: Divide both sides: \(\frac{2.1y}{2.1}=\frac{6.3}{2.1}\) - step6: Divide the numbers: \(y=3\) - step7: Substitute the value of \(y:\) \(x=3\times 3\) - step8: Calculate: \(x=9\) - step9: Calculate: \(\left\{ \begin{array}{l}x=9\\y=3\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}x=9\\y=3\end{array}\right.\) - step11: Rewrite: \(\left(x,y\right) = \left(9,3\right)\) The solution to the system of equations is \( x = 9 \) and \( y = 3 \). Therefore, the number of minutes for this trip is 9 and the number of miles is 3.