Question

a wireless carrier offers the following plans that a person is considering. the family plan: $88 monthly fee, unlimited talk and text on up to 5 lines, and data charges of $42 for each device for up to 2 gb of data per device. the mobile share plan: $176 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $31 for each device up to a shared total of 10 gb of data. use p 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 $ find the model of the total cost of the mobile share plan $ assuming they stay under their data limit, find the number of devices that would make the two plans equal in cost. devices if a family has 7 smart phones, which plan should they choose? the mobile share plan the family plan

Explanation:

Step1: Define cost - model for Family Plan

The Family Plan has a fixed monthly fee of $88 and a data - charge of $42 per device. Let $P$ be the number of devices. The total cost $C_F$ of the Family Plan is the sum of the fixed fee and the data - charge for all devices. So, $C_F=88 + 42P$.

Step2: Define cost - model for Mobile Share Plan

The Mobile Share Plan has a fixed monthly fee of $176 and a data - charge of $31 per device. Let $P$ be the number of devices. The total cost $C_M$ of the Mobile Share Plan is the sum of the fixed fee and the data - charge for all devices. So, $C_M=176+31P$.

Step3: Find the number of devices for equal cost

Set $C_F = C_M$.
\[

$$\begin{align*} 88 + 42P&=176+31P\\ 42P-31P&=176 - 88\\ 11P&=88\\ P& = 8 \end{align*}$$

\]

Step4: Decide the plan for 7 devices

For $P = 7$:
$C_F=88+42\times7=88 + 294=382$
$C_M=176+31\times7=176 + 217=393$
Since $C_F

Answer:

The model of the total cost of the Family Plan: $88 + 42P$
The model of the total cost of the Mobile Share Plan: $176+31P$
The number of devices that would make the two plans equal in cost: $8$
If a family has 7 smart phones, which plan should they choose: The Family Plan