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The problem provides two telephone plans with different pricing structures:

- **Plan 1** charges $26 per month for unlimited calls.
- **Plan 2** charges $17 per month plus $0.08 per call.

The task is to:

### a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.

Let **x** represent the number of monthly calls. We need to set up an inequality comparing the costs of the two plans.

- **Plan 1** costs: $ 26 $ (fixed price).
- **Plan 2** costs: $ 17 + 0.08x $.

For Plan 1 to be more economical than Plan 2, we need the cost of Plan 1 to be less than Plan 2. The inequality would be:
\[
26 < 17 + 0.08x
\]

Now, solve for **x**:

1. Subtract 17 from both sides:
\[
26 - 17 < 0.08x
\]
\[
9 < 0.08x
\]

2. Divide both sides by 0.08:
\[
x > \frac{9}{0.08}
\]
\[
x > 112.5
\]

So, **x > 112.5**. Since the number of calls must be a whole number, Plan 1 becomes more economical when the number of monthly calls exceeds **113**.

### b. Explanation of the answer to part a:

This means that if you make more than 113 calls in a month, Plan 1, with its fixed $26 rate, will be cheaper than Plan 2, which charges $17 plus $0.08 per call.

---

Would you like further details or clarifications?

### Follow-up questions:
1. How would the inequality change if Plan 1 had a higher fixed rate?
2. What happens if Plan 2 reduces the cost per call to $0.05 instead of $0.08?
3. Can you graph the cost functions of both plans and find their intersection?
4. What is the cost difference if 100 calls are made using Plan 1 and Plan 2?
5. Is there a scenario where both plans cost the same? If so, how many calls would that be?

#### Tip:
When comparing fixed costs versus variable costs, solving for the break-even point (where the costs are equal) helps in determining which option is more economical.

The telephone company offers two billing plans for local calls. Plan 1 charges $26 per month for unlimited calls and Plan 2 charges $17 per month plus $0.08 per call. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2. Explain the meaning of the answer.

Explore how to use inequalities to compare two telephone billing plans, Plan 1 and Plan 2. Learn to find the number of monthly calls needed for Plan 1 to be more economical than Plan 2. Suitable for students in Grades 6-8.

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