Question

A cell 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

Answer 1

13 months.

Explanation:

Let
`x` 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
`x` months =
`\ 65x`.

Total cost for
`x` months =
`65x+45`.

Company 2:

Activation fee = $ 175

Fee per month = $ 55

Therefore, fee for
`x` months =
`\ 55x`

Total cost for
`x` months =
`55x+175`.

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

`65x+45=55x+175\\ 65x-55x=175-45\\ 10x=130\\ x=(130)/(10)\\ x=13`

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