Question

Question: A cell phone company offers two different plans. Plan A costs \(80 per month for unlimited talk and text. Plan B costs \)0.20 per minute plus $0.10 per text message sent. You need to purchase a plan for your 14-year-old sister. Your sister currently uses 1,700 minutes and sends 1,600 texts each month.

1. What is your sister’s total cost under each of the two plans?
2. Suppose your sister doubles her monthly usage to 3,400 minutes and sends 3,200 texts. What is your sister’s total cost under each of the two plans?

Short answer

Answer

1. The total cost as per Plan A is $80

The total cost as per Plan B is $500

2. The total cost as per Plan A is $80

The total cost as per Plan B is $1,000

Step-by-step solution

Meaning of Total Cost

Total cost is the term used to describe all expenses incurred while investing, including the investment's cost and any commissions related to brokerage, taxes, licensing, and other fees associated with the transaction.

Determining total cost under each of the two plans

Step 2: Determining total cost under each of the two plans

Plan A

Regardless of the quantity and quality of calls and messages, plan A will continue, costing $80 in any circumstances.

Plan B

The total cost under plan B is calculated as follows:

$$\begin{gathered} \mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{a}\mathit{s}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{P}\mathit{l}\mathit{a}\mathit{n}\mathbf{}\mathit{B}\mathbf{=}\left(Totalnumberofminutes\times Perminutecost\right)\mathbf{+}\left(Totalnumberoftexts\times Pertextcost\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\left(1,700\times \$0.20\right)\mathbf{+}\left(1,600\times \$0.10\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{500} \end{gathered}$$

Determining total cost under each of the two plans

Plan A

The total cost under plan A is $80

Plan B

Total cost under plan B if call and text volumes double are calculated as follows:

$$\begin{gathered} \mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{}\mathit{a}\mathit{s}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{P}\mathit{l}\mathit{a}\mathit{n}\mathbf{}\mathit{B}\mathbf{=}\left(Totalnumberofminutes\times Perminutecost\right)\mathbf{+}\left(Totalnumberoftexts\times Pertextcost\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\left(3,400\times \$0.20\right)\mathbf{+}\left(3,200\times \$0.10\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000} \end{gathered}$$