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Question

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?