A wireless carrier offers the following plans that a person is considering.
The Family Plan: $90 monthly fee, unlimited talk and text on up to 8 lines, and data charges of $40 for each device for up
to 2 GB of data per device. The Mobile Share Plan: $120 monthly fee for up to 10 devices, unlimited talk and text for all
the lines, and data charges of $35 for each device up to a shared total of 10 GB of data. Use for the number of devices
that need data plans as part of their cost. Find the model of the total
cost of the Family Plan.

To model the total cost of the Family Plan, we need to consider the fixed monthly fee, the number of devices, and the data charges for each device.

Here are the components of the Family Plan:
- **Fixed monthly fee**: $90
- **Data charges**: $40 per device for up to 2 GB of data per device
- **Number of devices**: Let’s call this number $ n $, where $ n $ is up to 8 devices.

The total cost $ C $ of the Family Plan can be written as a function of $ n $ (the number of devices):

\[
C(n) = 90 + 40n
\]

Where:
- $ 90 $ is the fixed monthly fee,
- $ 40n $ is the cost for data per device.

### Example:
- If there are 3 devices on the plan, the total cost would be:
  \[
  C(3) = 90 + 40(3) = 90 + 120 = 210
  \]

Would you like more examples, further details on the model, or do you have any questions?

Here are 5 related questions that might interest you:
1. How would the total cost change if the Family Plan included an additional data charge for devices exceeding 2 GB?
2. What is the total cost if all 8 devices are on the Family Plan?
3. How does the Family Plan compare to the Mobile Share Plan for 5 devices?
4. How would the total cost change if there was a discount on the data charge for more than 4 devices?
5. Can we create a similar model for the Mobile Share Plan?

**Tip**: When comparing plans, it's useful to calculate the break-even point where one plan becomes cheaper than another.

A wireless carrier offers the following plans that a person is considering. The Family Plan: $90 monthly fee, unlimited talk and text on up to 8 lines, and data charges of $40 for each device for up to 2 GB of data per device. The Mobile Share Plan: $120 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $35 for each device up to a shared total of 10 GB of data. Use for the number of devices that need data plans as part of their cost. Find the model of the total cost of the Family Plan.

Learn how to calculate the total cost of a Family Plan offered by a wireless carrier, considering the monthly fee and data charges per device. This problem covers key algebraic concepts and cost analysis techniques suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation