Question

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?

Answer 1

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 $3$ GB, cost $=$ $$35$

For $4$ GB, cost $=$ $$35+$$$8=$$$43$

For $5$ GB, cost $=$ $$43+$$$8=$$$51$

For $6$ GB, cost $=$ $$51+$$$8=$$$59$

For $7$ GB, cost $=$ $$59+$$$8=$$$67$

For $8$ GB, cost $=$ $$67+$$$8=$$$75$

Carrier B

For $5$ GB, cost $=$ $$55$

For $6$ GB, cost $=$ $$55+$$$4=$$$59$

For $7$ GB, cost $=$ $$59+$$$4=$$$63$

For $8$ GB, cost $=$ $$63+$$$4=$$$67$

So, the cost of the two plans is same after $6$ 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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