Question
Madison took a taxi from her house to the airport. The taxi company charged a pick-up fee of \( \$ 3.20 \) plus \( \$ 5 \) per mile. The total fare was \( \$ 98.20 \), not including the tip. Write and solve an equation which can be used to determine \( m \), the number of miles in the taxi ride. Answer Attempt 1 out of 2 Equation: Answer: \( m=\square \)
Ask by Herrera Hilton. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The number of miles Madison traveled is 19 miles.
Solution
To determine the number of miles \( m \) Madison traveled in the taxi, we can set up and solve an equation based on the given information.
**Given:**
- **Pick-up fee:** \$3.20
- **Rate per mile:** \$5
- **Total fare:** \$98.20
**Step 1: Set Up the Equation**
The total fare is the sum of the pick-up fee and the cost per mile multiplied by the number of miles traveled.
\[
\text{Total Fare} = \text{Pick-up Fee} + (\text{Rate per Mile} \times m)
\]
Plugging in the known values:
\[
98.20 = 3.20 + 5m
\]
**Step 2: Solve for \( m \)**
Subtract the pick-up fee from both sides of the equation to isolate the term with \( m \):
\[
98.20 - 3.20 = 5m
\]
\[
95 = 5m
\]
Now, divide both sides by 5 to solve for \( m \):
\[
m = \frac{95}{5}
\]
\[
m = 19
\]
**Answer:**
\[
m = 19 \text{ miles}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
The total fare for the taxi ride can be expressed as the sum of the pick-up fee and the cost per mile multiplied by the number of miles. This means we can set up the equation: \[ 3.20 + 5m = 98.20 \] Now, we can solve for \( m \): 1. Subtract the pick-up fee from both sides: \[ 5m = 98.20 - 3.20 \] \[ 5m = 95 \] 2. Now, divide by 5: \[ m = \frac{95}{5} \] \[ m = 19 \] So, \( m = 19 \). Madison traveled 19 miles to the airport!
