A Third Option?

Question

The college student who is looking for a data plan for her cell phone found a third option, which also offers a 2 gigabyte monthly allowance for data.

The monthly cost of this option can be represented by function , defined by: , where  is the gigabytes of data used over the monthly allowance.

1. Find  and explain what it means in this situation.
2. Her budget is still $50 a month. To find out how many gigabytes of data she could use if she chose this plan, she writes  and solves for  What value of  makes this equation true? Show your reasoning.

Answer 1

The monthly cost of this third option is given by the equation C, and x is equal to the number of gigabytes of data used over this monthly allowance. Therefore, substituting 0.7 for x, we can write the equation as:

C = 30(0.7) + 5

Solving for C, we will get 26 as an answer, and this will represent how much monthly it will cost this student to use 0.7 gigabytes of data over her monthly limit. So, if she goes 0.7 gigabytes over her monthly limit, it will cost her $26 more than what she would normally pay.

As we learn in part two, she has a budget of $50 a month. To determine the exact number of gigabytes she can use, lets solve for x, and set the equation equal to 50.

50 = 30x + 5

45 = 30x

x = 1.5 gigabytes of data.

Remember what x represents. A common mistake could be saying that she can use 1.5 gigabytes of data for $50, but this would be incorrect. x is equal to the gigabytes of data over the monthly allowance.

As we learn in the problem, her monthly allowance is 2 gigabytes. So, 2 + 1.5 = 3.5 gigabytes of data that she can afford with her monthly budget.

Answer 2

C(0.7) = 30(0.7) + 5 = 21 + 5 = 26

If the cell phone plan allows 0.7 gigabytes of data monthly, then she will pay $26.

C(x) = 30x + 5 = 50

Subtract 5 on both sides → 30x = 45

Divide 30 on both sides → x = 1.5

She will use 1.5 gigabytes of data for her cell phone plan in order to pay $50 monthly.

Problem #1 gives you the input, x. Find the output, C(x).

Problem #2 gives you the output, C(x). Find the input, x.