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.