Acell phone company charges a $45 activation fee and $65 per month for their monthly plan. another cell phone company charges $55 per month and a $175 activation fee for their monthly plan.

the number of months it takes for the plans to cost the same is months

13 months.

Step-by-step explanation:

Let be the number of months it takes for the plans to cost the same.

Company 1:

Activation fee = $ 45

Fee per month = $ 65

Therefore, fee for months = .

Total cost for months = .

Company 2:

Activation fee = $ 175

Fee per month = $ 55

Therefore, fee for months =

Total cost for months = .

Now, the total cost for both the companies are same if,

Therefore, after 13 months, the cost for both the companies will be same.