A taxi service charges a flat fee of [tex]\[tex]$ 1.25[/tex] and [tex]\$[/tex] 0.75[/tex] per mile. If Henri has [tex]\$ 14.00[/tex], which of the following shows the number of miles he can afford to ride in the taxi?

A. [tex]m \leq 17[/tex]
B. [tex]m \geq 17[/tex]
C. [tex]m \leq 20.3[/tex]
D. [tex]m \geq 20.3[/tex]



Answer :

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.