Car rental agency A charges $50 per day plus 10 cents per mile driven. Agency B charges $20 per day plus 30 cents per mile driven. 

When will car rental agency A be cheaper than car rental agency B for a one-day rental?

Responses
A	With a one-day rental, if you drive more than 50 miles, then car rental agency A will be cheaper than car rental agency B.With a one-day rental, if you drive more than 50 miles, then car rental agency A will be cheaper than car rental agency B.
B	With a one-day rental, if you drive more than 100 miles, then car rental agency A will be cheaper than car rental agency B.With a one-day rental, if you drive more than 100 miles, then car rental agency A will be cheaper than car rental agency B.
C	With a one-day rental, you must drive more than 175 miles for car rental agency A to be cheaper than car rental agency B.With a one-day rental, you must drive more than 175 miles for car rental agency A to be cheaper than car rental agency B.
D	With a one-day rental, you must drive more than 150 miles for car rental agency A to be cheaper than car rental agency B.

Let's compare the costs for a one-day rental from both car rental agencies, and determine when Agency A is cheaper than Agency B.

### Agency A:
- Charges $50 per day plus 10 cents per mile.
- The cost for driving $ x $ miles is:
\[
\text{Cost of A} = 50 + 0.10x
\]

### Agency B:
- Charges $20 per day plus 30 cents per mile.
- The cost for driving $ x $ miles is:
\[
\text{Cost of B} = 20 + 0.30x
\]

To find when Agency A is cheaper than Agency B, we need to solve:
\[
50 + 0.10x < 20 + 0.30x
\]

### Step-by-step solution:
1. Subtract $ 0.10x $ from both sides:
\[
50 < 20 + 0.20x
\]
2. Subtract 20 from both sides:
\[
30 < 0.20x
\]
3. Divide both sides by 0.20:
\[
150 < x
\]

So, **Agency A will be cheaper if you drive more than 150 miles**.

The correct answer is:
**D: With a one-day rental, you must drive more than 150 miles for car rental agency A to be cheaper than car rental agency B.**

---

Would you like further details or have any questions about this?

### 5 Related Questions:
1. What if the rental period is more than one day? How would the costs compare then?
2. How would the answer change if Agency B's per-mile charge decreased to 25 cents?
3. What is the break-even point where both agencies cost the same for a one-day rental?
4. What happens to the comparison if both agencies offer a discount for long-distance travel?
5. How would the comparison change if there is an additional flat fee, like insurance?

**Tip:** When comparing linear costs like this, break-even points occur where the equations for both options are equal, and solving for that can clarify the decision-making process.

Car rental agency A charges $50 per day plus 10 cents per mile driven. Agency B charges $20 per day plus 30 cents per mile driven. When will car rental agency A be cheaper than car rental agency B for a one-day rental?

Find out when car rental agency A is cheaper than agency B with this detailed comparison of costs. This problem involves solving linear inequalities to compare rental charges, helping students practice algebraic concepts. Perfect for students in Grades 6-8.

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