Question

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. 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.

Answer 1

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 :

$M_1 = 60x + 350$

Money-time relation of plan T-Mobile :

$M_2 = 80y + 275$

( 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, $M_2\ge M_1$

$80t+275 \ge 60t + 350\\\\20t \ge 350 - 275\\\\20t \ge 75\\\\t \ge 3.75$

Hence, this is the required solution.