Question

The cost of a taxi ride is an initial fee plus \(\$ 1.50\) for each mile. Your fare for 9 miles is \(\$ 15.50 .\) Write an equation that models the total cost \(y\) of a taxi ride in terms of the number of miles \(x\).

Short answer

The equation that models the total cost \(y\) of a taxi ride in terms of the number of miles \(x\) is \(y = 1.50x + 2\)

Step-by-step solution

Understand the given data

First, interpret the given data. A taxi ride costs $1.50 per mile after a certain initial fee. For a 9-mile ride, the total cost is $15.50, including the initial fee.

Form an initial equation

Assume the initial fee to be \(b\). The equation then is \(y = 1.50 \times x + b\) (This equation represents the total taxi fare (y) in terms of number of miles (x), where the $1.50 is the rate per mile and b is the initial flat fee.) Then substitute the given values into the equation to solve for \(b\), i.e., \(15.50 = 1.50 \times 9 + b\).

Solve the equation

Simplify the equation to find the initial rate (b). To do this, perform the multiplication on the right side of the equation and then isolate b by subtracting the result from both sides. The simplified equation becomes: \(15.50 = 13.50 + b\). Now, subtract 13.5 from both sides, \(b=15.50 - 13.50\). After performing this subtraction, \(b= 2\) .

Form a Final Equation

Substitute the initial fee \(b\) into the original equation, which is \(y = 1.50x + b\). So, the final equation which models the total cost \(y\) of a taxi ride in terms of the number of miles \(x\) will be \(y = 1.50x + 2\)