Question

A cell phone provider offers a plan that costs ​$30 per month plus ​$0.20 per text message sent or received. A comparable plan costs ​$60 per month but offers unlimited text messaging. Complete parts a. and b. below.
a. How many text messages would have to be sent or received in order for the plans to cost the same each​ month?
In order for the plans to cost the​ same,? nothing text messages would have to be sent or received. ​(Simplify your answer. Type an integer or a​ decimal.)

Answer 1

The first plan has a fixed cost, $30, and a cost per text message of $0.20.
If you sent t number of text messages, the cost per message is $0.20t.
The total cost of the first plan is

0.2t + 30

The second plan simply costs $60 no matter how many texts you used.
The second plan costs

60

Set the two costs equal to each other to find out how many messages you need to send with the first plan to cost the same as the second plan.

0.2t + 30 = 60

0.2t = 30

t = 150

If you use exactly 150 text messages, the plans cost the same.
If you use fewer than 150 text messages, the first plan costs less.
If you use more than 150 text messages, the firs plan costs more.

Answer 2

5 times 30 = 150 text messages

Fewer - lower Equal to - same More - higher