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The problem you've shared involves linear inequalities. Let's break it down:

The taxi charges:
- A flat rate of $1.95
- An additional $0.54 per mile

Katie has a budget of $23 to spend on the ride. We need to find out how many miles she can travel without exceeding this limit.

### Step-by-step solution:

1. **Set up the inequality**:
   \[
   1.95 + 0.54x \leq 23
   \]
   Here, $x$ represents the number of miles Katie can travel.

2. **Solve for $x$**:
   - First, subtract the flat rate from both sides:
     \[
     0.54x \leq 23 - 1.95
     \]
     \[
     0.54x \leq 21.05
     \]
   - Now, divide both sides by 0.54:
     \[
     x \leq \frac{21.05}{0.54}
     \]
     \[
     x \leq 38.98
     \]

3. **Interpret the result**:
   Since Katie can't travel a fraction of a mile, we round down to the nearest whole number. Therefore, the maximum number of miles Katie can travel without exceeding her budget is **38 miles**.

The correct answer is **38**.

Would you like more details on any step, or do you have further questions?

Here are 5 related questions for further practice:
1. What if Katie's budget was $30 instead of $23? How many miles could she travel then?
2. If the per-mile charge increased to $0.60, how would that affect the maximum number of miles?
3. What if the flat rate increased to $2.50 but the per-mile rate stayed the same?
4. How would the equation change if Katie could only spend up to $20 on the ride?
5. What if the per-mile charge was reduced to $0.50? How many miles could Katie travel now?

**Tip:** When solving inequalities, always check if rounding is needed, especially when dealing with real-world scenarios like distance or money.

Green's Taxi charges a $1.95 flat rate for a ride in the cab. In addition to that, they charge $0.54 per mile. Katie has no more than $23 to spend on a ride. At most, how many miles can Katie travel without exceeding her spending limit?

This problem involves linear inequalities where we calculate how many miles Katie can travel given a flat taxi fare of $1.95, a per-mile charge of $0.54, and a maximum budget of $23. Detailed steps to solve this inequality are provided, suitable for Grades 7-9.

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