https://file.aiquickdraw.com/mathbot/file/172670863018798xwihz0.jpg

Let's analyze and break down the problem:

We have two car rental companies, A and B:

- **Company A** charges $45 per day to rent a car.
- **Company B** charges $30 per day plus $0.20 per mile driven.

The question asks: For how many miles driven is the cost at **Company B** more than the cost at **Company A** for a one-day rental?

### Step 1: Set up the cost equations
Let $ x $ be the number of miles driven.

- **Company A** charges $45 for a day regardless of miles, so its total cost is:
  \[
  C_A = 45
  \]

- **Company B** charges $30 per day plus $0.20 per mile, so its total cost is:
  \[
  C_B = 30 + 0.20x
  \]

### Step 2: Write the inequality
We want to find when the cost of Company B is greater than the cost of Company A, so we set up the inequality:
\[
30 + 0.20x > 45
\]

### Step 3: Solve the inequality
Now, solve for $ x $:

1. Subtract 30 from both sides:
   \[
   0.20x > 15
   \]

2. Divide both sides by 0.20:
   \[
   x > \frac{15}{0.20}
   \]

3. Simplify:
   \[
   x > 75
   \]

### Conclusion
The cost at **Company B** will be greater than the cost at **Company A** when the number of miles driven exceeds **75 miles**.

---

Would you like more details on how I solved this, or do you have any further questions?

### Related Questions:
1. How would the inequality change if Company A charged by the mile?
2. What if Company B charged a higher per-mile rate, say $0.30 per mile?
3. How would the solution change if Company A's daily rate increased?
4. What if Company B had an additional flat fee?
5. How can you represent this comparison graphically?

**Tip:** Always check the units and make sure they match when comparing costs!

Car rental company A charges $45 a day to rent a certain car. Car rental B charges $30 a day plus $0.20 per mile to rent a similar car. For how many miles is the cost at car rental company B more than the cost at car rental company A for a one-day rental?

Learn how to solve the inequality comparing car rental costs between Company A, which charges $45 per day, and Company B, which charges $30 per day plus $0.20 per mile. Find out the number of miles at which Company B becomes more expensive. Suitable for Grades 7-9.

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