https://file.aiquickdraw.com/mathbot/file/17284331130799eae33sw.jpg

From the image you provided, we have a problem related to comparing two pricing options (Option A and Option B) for renting a car. The cost (in dollars) depends on the number of miles driven.

### Here's a breakdown of the task:

1. **Part (a)** asks:
   - If Lisa drives 150 miles, which option costs less?
   - By how much does it cost less than the other option?

2. **Part (b)** asks:
   - For what number of miles do the two options cost the same?
   - If Lisa drives more than this amount, which option costs less?

### Observations from the graph:
- **Option A** appears as a red line with a steeper slope (indicating higher cost per mile).
- **Option B** is a blue line, flatter than Option A (indicating a lower cost per mile for longer distances).

Let’s solve these step-by-step:

### Part (a):
- At 150 miles, you can estimate from the graph that **Option A** is more expensive than **Option B**.
- To determine how much less Option B costs, you would look at the vertical difference (cost difference) between the two lines at the 150-mile mark.

### Part (b):
- The point where the two lines intersect is the point where both options cost the same. This happens around **100 miles** (estimated from the graph).
- If Lisa drives more than 100 miles, **Option B** will be cheaper because its line increases at a slower rate compared to Option A.

Would you like more details on any of these calculations or comparisons?

### 5 related questions:
1. What is the exact cost equation for both Option A and Option B?
2. How can you calculate the intersection point algebraically?
3. How do the slopes of the two lines represent cost per mile?
4. At what mileage will Option A cost double that of Option B?
5. Can we create a general formula for determining which option is cheaper based on miles driven?

### Tip:
When comparing costs, look for the point where two cost functions intersect; this helps determine at what quantity (in this case, miles) the costs become equal.

Lisa will rent a car for a day. The rental company offers two pricing options: Option A and Option B. For each pricing option, the cost (in dollars) depends on miles driven, as shown on the graph. The questions ask: (a) If Lisa drives 150 miles, which option costs less and by how much? (b) At what number of miles do the two options cost the same, and which option is cheaper beyond that point?

Explore how to compare two car rental pricing options using graphs. This problem involves interpreting cost functions based on miles driven, identifying the point of intersection, and determining which option is cheaper beyond a certain mileage. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation