https://file.aiquickdraw.com/mathbot/file/17281856521742qafvafs.jpg

Let's analyze the graph and questions provided in the image.

### Plans:
- **Plan A (blue line)** increases linearly as minutes used increase.
- **Plan B (red line)** remains constant, showing a flat rate, regardless of the minutes used.

### Question (a):
For 450 minutes, which plan costs more and by how much?

1. **Plan A:**
   - From the graph, Plan A increases linearly. At 450 minutes, it appears to reach approximately $36.

2. **Plan B:**
   - Plan B has a flat cost of $24 regardless of the minutes used.

**Difference:**  
Plan A costs $36, and Plan B costs $24 for 450 minutes.  
So, **Plan A costs $12 more** than Plan B.

### Question (b):
At what number of minutes do the two plans cost the same, and which plan costs less if the minutes are below this amount?

1. To find where the two plans cost the same, look for the intersection of the two lines on the graph. It seems to occur around **240 minutes**.

2. For fewer than 240 minutes:
   - **Plan A** increases linearly, so its cost will be less than Plan B (which is always $24) before they intersect.
   - Therefore, for less than 240 minutes, **Plan A costs less**.

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Would you like further details or explanations?

Here are five related questions you might consider:
1. How is the cost-per-minute calculated for Plan A?
2. What happens if the usage exceeds 500 minutes in Plan A? Does the pattern hold?
3. How does Plan A's cost change compared to Plan B at lower usage, say 100 minutes?
4. How could a user decide between the plans based on their expected usage?
5. What other factors (besides cost) might influence the choice between these two plans?

**Tip:** When comparing linear vs. fixed costs, the point of intersection is crucial—it tells you at what usage the linear cost becomes more expensive.

If Aldo makes 450 minutes of long distance calls, which plan costs more and by how much? For what number of minutes do both plans cost the same, and which plan is cheaper below that amount?

Explore the cost comparison between two long-distance call plans—Plan A (linear cost) and Plan B (constant cost). This problem calculates the cost for 450 minutes, finds where both plans cost the same, and identifies which plan is cheaper for different usage levels.

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