Which Companies Data Plan is the better deal...?

Question

Your business is trying to buy internet services for its office. There are three different companies to choose from and each offers a different plan.

Company A: You can pay $200 per mont for unlimited internet use.

Company B: You pay $30 per month plus $0.50 per GB of data

Company C: You pay $50 per month for the first 100GB and then pay $1 per additional GB of data over an above that first 100 GB.

Set up and solve a linear inequality to determine for what number of GB of data usage will Company A be better than Company B?
Set up and solve a linear inequality to determine for what number of GB of data usage will Company C be better than Company B?
If your business expects to use 300GB of data over the next month, which company should it go with? What if it expects to use 500GB?

Answer 1

Set up and solve a linear inequality to determine for what number of GB of data usage will Company A be better than Company B?

0.5x + 30 < 200

        - 30 =  -30

________   ____

 

0.5x        < 170

 

     x        < 340

 

So if using more than 340 then it might be best for you to buy from A.  But the question is unclear because it might be asking if A would benefit more from servicing you.

 

 

Next Question: Set up and solve a linear inequality to determine for what number of GB of data usage will Company C be better than Company B?

 

Again the question is unclear and I really hate spending time only to find out I answered the wrong question.

 

But I think the solution is as follows:

 Company C.plan    <  Company B plan

 

 1(x - 100) + 50      <   0.5x  +  30

 

       x -  50             <   0.5x  +  30

          + 50             =           +  50

      _____                   __________

      x                      <   0.5x  +  80

-0.5x                      =  -0.5x

_____                         __________

 0.5x                       <               80

 

     x                        <             160

 

So Company C represented by the 1(x - 100) + 50 plan is best for the buyer if using less than 160 GB.

 

 

I think the last question is clearly stated.  I believe it is easy.  Just sub.in the values of 300 and 500 for x into the algebraically represented plans and see which comes up less ..... for y

 

Company A: y = 200, the total cost per month, no matter how many GB used.

Company B: 0.5x + 30 = y

Company C: 1(x - 100) + 50 = y