Question

A taxi service charges $3.00 just to get in the cab and $1.00 for each mile traveled.
Use the calculator to help you solve for the cost per mile.
Number of miles (m) Cost in dollars (c) Cost per mile (
m
c
​
)
5 $8.00
8 $11.00
20 $23.00

Answer 1

To find the total cost (c) given the number of miles (m) this taxi service charges, we can use the following formula based on the fare structure:

\[
c = 3 + 1 \times m
\]

Where:
- \(c\) is the total cost in dollars,
- \(3\) is the initial charge for getting in the cab,
- \(1\) is the charge per mile,
- \(m\) is the number of miles traveled.

Let's calculate the costs for the provided number of miles and then find the cost per mile.

### 1. For 5 miles:
\[
c = 3 + 1 \times 5 = 3 + 5 = 8
\]
- Cost per mile:
\[
\text{Cost per mile} = \frac{c}{m} = \frac{8}{5} = 1.60 \text{ dollars per mile}
\]

### 2. For 8 miles:
\[
c = 3 + 1 \times 8 = 3 + 8 = 11
\]
- Cost per mile:
\[
\text{Cost per mile} = \frac{c}{m} = \frac{11}{8} = 1.375 \text{ dollars per mile}
\]

### 3. For 20 miles:
\[
c = 3 + 1 \times 20 = 3 + 20 = 23
\]
- Cost per mile:
\[
\text{Cost per mile} = \frac{c}{m} = \frac{23}{20} = 1.15 \text{ dollars per mile}
\]

### Summary of Results:
- **For 5 miles:** Total cost is $8.00, Cost per mile is $1.60
- **For 8 miles:** Total cost is $11.00, Cost per mile is $1.375
- **For 20 miles:** Total cost is $23.00, Cost per mile is $1.15

The cost per mile decreases as more miles are traveled, due to the fixed initial charge.