A wireless carrier offers the following plans that a person is considering.
The Family Plan: $70 monthly fee, unlimited talk and text on up to 5 lines, and data charges of $50 for each device for up to 2 GB of data per device.

The Mobile Share Plan: $150 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $10 for each device up to a shared total of 10 GB of data.
Find the model of the total cost of the Family Plan in dollars. Use P for the number of devices that need data plans as part of their cost.

To model the total cost of the Family Plan, we need to account for both the monthly fee and the data charges.

1. **Monthly Fee**: The Family Plan has a fixed monthly fee of $70.

2. **Data Charges**: The plan charges $50 for each device that uses data, with each device being allowed up to 2 GB of data.

Let $ P $ represent the number of devices that need data plans.

### Model the Total Cost:

The total cost $ C $ of the Family Plan can be expressed as:

\[
C = 70 + 50P
\]

Where:
- $ C $ is the total monthly cost in dollars.
- $ 70 $ is the fixed monthly fee.
- $ 50P $ represents the total data charges for $ P $ devices.

Thus, the model for the total cost of the Family Plan is:

\[
C = 70 + 50P
\]

This formula allows you to calculate the total monthly cost based on the number of devices that require data.

Would you like further details or have any questions? Here are some related questions:

1. How would the cost model change if the data charges per device were increased?
2. What would be the total cost if $ P = 3 $?
3. How does the Family Plan compare to the Mobile Share Plan for different values of $ P $?
4. If a device exceeds 2 GB of data, how would the cost model adjust?
5. How would the cost change if an additional line (without data) is added?

**Tip:** When comparing plans, consider both the fixed costs and the variable costs (like data charges) to determine which plan is more economical for your specific needs.

Understand how to model the total cost of a wireless carrier's Family Plan, including a $70 fixed monthly fee and $50 data charges per device up to 2 GB. Use the formula C = 70 + 50P to calculate the monthly cost based on the number of devices needing data.

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