Given :
AT&T charges $350 to get a plan with them, plus $60 per month.
T-Mobile charges a $275 initial fee, plus $80 per month.
To Find :
Write an equation or inequality that can be used to determine the number of months it would take for T-Mobile to cost the same or more than AT&T.
Solution :
Money-time relation of plan AT&T :
[tex]M_1 = 60x + 350[/tex]
Money-time relation of plan T-Mobile :
[tex]M_2 = 80y + 275[/tex]
( Here, x and y are number of months )
Let, after t months would take for T-Mobile to cost the same or more than AT&T.
So, [tex]M_2\ge M_1[/tex]
[tex]80t+275 \ge 60t + 350\\\\20t \ge 350 - 275\\\\20t \ge 75\\\\t \ge 3.75[/tex]
Hence, this is the required solution.
