Question

The cost of a taxi ride is an initial fee plus \(\$ 1.50\) for each mile. Your fare for 9 miles is \(\$ 15.50 .\) How much is the initial fee?

Short answer

The initial fee is $2.

Step-by-step solution

Create the equation

Let’s denote the initial fee as x. So the cost of the taxi ride is \(x + 1.5 \times \text{number of miles}\). For a 9-mile ride, which costs \(\$15.50), the equation would be \(x + 1.5*9 = 15.5\).

Solve the equation

To solve for x, we will follow the order of operations (PEMDAS/BODMAS). First, calculate \(1.5 * 9 = 13.5\). The equation now reads \(x + 13.5 = 15.5\). To isolate x, subtract 13.5 from both sides of the equation to get \(x = 15.5 - 13.5\).

Evaluate result

Subtract to get the final result: \(x = 2\).