The table shows two options provided by high speed internet. option 1 have set up fee of $50 with $30 per month. option 2 have no set up fee and is $40 per month. in how many months will the total cost of both options be the same? what will that cost be? if you plan to cancel your internet service after 9 months, which is the cheaper option?

Let us take the case of first option first
Set up fee that need to paid = $50
Per month charge of using internet = $30
Now let us take the case of the second option
Set up fee that need to be paid = $0
Per month charge of using the internet = $40
Let us assume the number of months after which both options will be same = x
Then
50 + 30x = 40x
40x - 30x = 50
10x = 50
x = 50/10
   = 5
So after 5 months both the options will be same
Now to find the cost after 5 months
we can take any option for calculating = 40x
                                                              = (40 * 5) dollars
                                                              = 200 dollars
So after 5 months that amount that need to be paid is $200 for any of the plans
In case of the first option, 
Cost after 9 months = 50 + 30x
                                 = 50 + (30 * 9)
                                 = 50 + 270
                                 = 320 dollars
After 9 months the cost using second option = 40x
                                                                        = (40 * 9)
                                                                        = 360 dollars
So after 9 months the first option will be cheaper.