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Part 1
The telephone company offers two billing plans for local calls. Plan 1 charges ​$38 per month for unlimited calls and Plan 2 charges ​$19 per month plus ​$0.04 per call.

Answer 1

To analyze the two billing plans for local calls, we can set up equations to represent the costs of each plan based on the number of calls made in a month.

**Plan 1:**
- Cost = $38 (unlimited calls)

**Plan 2:**
- Cost = $19 + $0.04 × (number of calls)

### Let's define the cost equations based on the number of calls (let \( x \) be the number of calls):

- For Plan 1: \( C_1 = 38 \)
- For Plan 2: \( C_2 = 19 + 0.04x \)

### To find when the two plans cost the same:

Set the two cost equations equal to each other:

\[
38 = 19 + 0.04x
\]

### Now solve for \( x \):

1. Subtract 19 from both sides:
\[
38 - 19 = 0.04x
\]
\[
19 = 0.04x
\]

2. Divide both sides by 0.04:
\[
x = \frac{19}{0.04}
\]
\[
x = 475
\]

### Conclusion:
- The two plans are equal in cost when you make **475 calls** in a month.
- If you make fewer than 475 calls, Plan 2 is cheaper. If you make more than 475 calls, Plan 1 is the better option.

Would you like to explore a specific scenario or additional information about these plans?