Sure, let's solve this problem step by step.
### Step 1: Identify the Components
Henri wishes to take a ride in a taxi which charges:
1. A flat fee of \$1.25.
2. \$0.75 per mile.
Henri has a total of \$14.00 to spend.
### Step 2: Determine the Cost After Paying the Flat Fee
First, Henri needs to pay the flat fee of \$1.25. Therefore, the amount of money he has left after paying the flat fee is:
[tex]\[ 14.00 - 1.25 = 12.75 \][/tex]
### Step 3: Calculate the Number of Miles Henri Can Afford
The remaining amount of money (\[tex]$12.75) will be used to pay for the miles driven, at a rate of \$[/tex]0.75 per mile. Therefore, we need to calculate how many miles he can afford:
[tex]\[ \text{Number of miles} = \frac{\text{Money left}}{\text{Cost per mile}} \][/tex]
[tex]\[
\text{Number of miles} = \frac{12.75}{0.75} = 17.0
\][/tex]
### Step 4: Interpret the Results
Now we need to determine which of the given inequalities Henri's mileage fits into.
1. \( m \leq 17 \)
- Since Henri can ride 17 miles, this inequality holds true. Henri can ride up to 17 miles.
2. \( m \geq 17 \)
- Again, since Henri can exactly afford to ride 17 miles, this inequality also holds true.
3. \( m \leq 20.3 \)
- 17 miles is definitely less than or equal to 20.3 miles, so this inequality is true.
4. \( m \geq 20.3 \)
- 17 miles is less than 20.3 miles, so this inequality is false.
### Conclusion
The correct results based on Henri's financial situation are:
- \( m \leq 17 \) is true.
- \( m \geq 17 \) is true.
- \( m \leq 20.3 \) is true.
- \( m \geq 20.3 \) is false.
So, Henri can afford to ride exactly 17 miles with his \$14.00 budget.
