11. You are fed up with your cell phone plan and are thinking of switching carriers. Carrier A is offering a $35 per month plan with 3 GB (gigabytes) of data and then a charge of $8 per additional GB of data after that. Similarly, Carrier B is offering a $55 per month plan with 5 GB of data and then a charge of $4 per additional GB of data after that.a. In a given month, after how much data use would the two plans cost the same?b. If you historically use an average of 6 GB of data, which plan should you choose?c. Which plan is cheaper in the long run?

Respuesta :

The cost of the two plans is same after 6 GB of data use.

Both the plan cost the same for 6 GB of data use. So, you can use any one of the two data plans.

Plan B is cheaper in the long run.

A) Carrier A

For [tex]3[/tex] GB, cost [tex]=[/tex] $[tex]35[/tex]

For [tex]4[/tex] GB, cost [tex]=[/tex] $[tex]35+[/tex]$[tex]8=[/tex]$[tex]43[/tex]

For [tex]5[/tex] GB, cost [tex]=[/tex] $[tex]43+[/tex]$[tex]8=[/tex]$[tex]51[/tex]

For [tex]6[/tex] GB, cost [tex]=[/tex] $[tex]51+[/tex]$[tex]8=[/tex]$[tex]59[/tex]

For [tex]7[/tex] GB, cost [tex]=[/tex] $[tex]59+[/tex]$[tex]8=[/tex]$[tex]67[/tex]

For [tex]8[/tex] GB, cost [tex]=[/tex] $[tex]67+[/tex]$[tex]8=[/tex]$[tex]75[/tex]

Carrier B

For [tex]5[/tex] GB, cost [tex]=[/tex] $[tex]55[/tex]

For [tex]6[/tex] GB, cost [tex]=[/tex] $[tex]55+[/tex]$[tex]4=[/tex]$[tex]59[/tex]

For [tex]7[/tex] GB, cost [tex]=[/tex] $[tex]59+[/tex]$[tex]4=[/tex]$[tex]63[/tex]

For [tex]8[/tex] GB, cost [tex]=[/tex] $[tex]63+[/tex]$[tex]4=[/tex]$[tex]67[/tex]

So, the cost of the two plans is same after [tex]6[/tex] GB of data use.

B) Here, both the plan cost the same for 6 GB of data use. So, you can use any one of the two data plans.

C) Clearly plan B is cheaper in the long run.

Learn more about linear equations here.

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