Question

for the following exercises, use this scenario: 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 p for the number of devices that need data plans as part of their cost. 13. find the model of the total cost of the family plan. 14. find the model of the total cost of the mobile share plan. 15. assuming they stay under their data limit, find the number of devices that would make the two plans equal in cost. 16. if a family has 3 smart phones, which plan should they choose?

Explanation:

Step1: Define variables and fixed - costs

Let $P$ be the number of devices. The Family Plan has a fixed monthly fee of $\$90$ and a data - charge of $\$40$ per device.
The cost function for the Family Plan $C_F$ is the sum of the fixed fee and the data - charge for $P$ devices.
$C_F=90 + 40P$

Step2: Define the cost function for the Mobile Share Plan

The Mobile Share Plan has a fixed monthly fee of $\$120$ and a data - charge of $\$35$ per device.
The cost function for the Mobile Share Plan $C_M$ is $C_M = 120+35P$

Step3: Find the number of devices for equal cost

Set $C_F = C_M$:
\[

$$\begin{align*} 90 + 40P&=120+35P\\ 40P-35P&=120 - 90\\ 5P&=30\\ P&=6 \end{align*}$$

\]

Step4: Evaluate the plans for $P = 3$

For the Family Plan with $P = 3$:
$C_F=90+40\times3=90 + 120=\$210$
For the Mobile Share Plan with $P = 3$:
$C_M=120+35\times3=120 + 105=\$225$

Answer:

1. $C_F=90 + 40P$
2. $C_M = 120+35P$
3. 6
4. The Family Plan