For the family plan:
Let:
y1 = Total cost
a1 = Charge for each device = 40
b1 = Monthly fee = 90
P = Number of devices
So:
The model for the family plan will be given by:
[tex]\begin{gathered} y1=a1P+b1 \\ y1=40P+90 \end{gathered}[/tex]For the Mobile share plan:
Let:
y2 = Total cost
a2 = Charge for each device = 35
b2 = Monthly fee = 120
P = Number of devices
The model for the mobile share plan will be given by:
[tex]\begin{gathered} y2=a2P+b2 \\ y2=35P+120 \end{gathered}[/tex]We can find the number of devices that would make the two plans equal in cost. Solving for:
[tex]\begin{gathered} y1=y2 \\ 40P+90=35P+120 \\ solve_{\text{ }}for_{\text{ }}P\colon \\ 40P-35P=120-90 \\ 5P=30 \\ P=\frac{30}{5} \\ P=6 \end{gathered}[/tex]The number of devices that would make the two plans equal in cost is 6.
If P = 3
[tex]\begin{gathered} y1=40(3)+90=210 \\ y2=35(3)+120=225 \end{gathered}[/tex]For 3 devices The family plan cost $210 and for 3 devices the mobile share plan cost $225, Therefore we can conclude that for 3 devices The family plan is more affordable.