Question
A taxi service charges $3.00 just to get in the cab and $1.00 for each mile traveled.
What do you notice about the cost per mile for each of the distances traveled?
Number of miles (m) Cost in dollars (c) Cost per mile (
m
c
)
5 $8.00 1.6
8 $11.00 1.375
20 $23.00 1.15
The cost per mile is not the same for the distances traveled.
The cost per mile is the same.
What do you notice about the cost per mile for each of the distances traveled?
Number of miles (m) Cost in dollars (c) Cost per mile (
m
c
)
5 $8.00 1.6
8 $11.00 1.375
20 $23.00 1.15
The cost per mile is not the same for the distances traveled.
The cost per mile is the same.
Answers
GPT-4o mini
To analyze the cost per mile for the distances traveled, let's break down the information given:
**Cost Equation:** The cost \( c \) of traveling \( m \) miles is given by the formula:
\[ c = 3 + 1 \cdot m \]
where \$3.00 is the base fare for getting into the cab and \$1.00 is charged for each mile traveled.
We can calculate the cost per mile for each scenario:
1. **For 5 miles:**
\[
c = 3 + 1 \cdot 5 = 8 \text{ dollars}
\]
Cost per mile:
\[
\text{Cost per mile} = \frac{8}{5} = 1.6 \text{ dollars/mile}
\]
2. **For 8 miles:**
\[
c = 3 + 1 \cdot 8 = 11 \text{ dollars}
\]
Cost per mile:
\[
\text{Cost per mile} = \frac{11}{8} = 1.375 \text{ dollars/mile}
\]
3. **For 20 miles:**
\[
c = 3 + 1 \cdot 20 = 23 \text{ dollars}
\]
Cost per mile:
\[
\text{Cost per mile} = \frac{23}{20} = 1.15 \text{ dollars/mile}
\]
Based on the calculations, we can see the cost per mile for each distance:
- 5 miles: \$1.60/mile
- 8 miles: \$1.375/mile
- 20 miles: \$1.15/mile
From these results, the cost per mile decreases as the distance traveled increases.
### Conclusion:
The correct statement is:
- **The cost per mile is not the same for the distances traveled.**
**Cost Equation:** The cost \( c \) of traveling \( m \) miles is given by the formula:
\[ c = 3 + 1 \cdot m \]
where \$3.00 is the base fare for getting into the cab and \$1.00 is charged for each mile traveled.
We can calculate the cost per mile for each scenario:
1. **For 5 miles:**
\[
c = 3 + 1 \cdot 5 = 8 \text{ dollars}
\]
Cost per mile:
\[
\text{Cost per mile} = \frac{8}{5} = 1.6 \text{ dollars/mile}
\]
2. **For 8 miles:**
\[
c = 3 + 1 \cdot 8 = 11 \text{ dollars}
\]
Cost per mile:
\[
\text{Cost per mile} = \frac{11}{8} = 1.375 \text{ dollars/mile}
\]
3. **For 20 miles:**
\[
c = 3 + 1 \cdot 20 = 23 \text{ dollars}
\]
Cost per mile:
\[
\text{Cost per mile} = \frac{23}{20} = 1.15 \text{ dollars/mile}
\]
Based on the calculations, we can see the cost per mile for each distance:
- 5 miles: \$1.60/mile
- 8 miles: \$1.375/mile
- 20 miles: \$1.15/mile
From these results, the cost per mile decreases as the distance traveled increases.
### Conclusion:
The correct statement is:
- **The cost per mile is not the same for the distances traveled.**