Comparing Two Mobile Phone Plans
A student compares two phone plans. Plan A costs $25 per month and includes 10 GB of data; extra data costs $8 per GB (charged in whole gigabytes). Plan B costs $40 per month and includes 30 GB; extra data costs $5 per GB. The student uses about 18 GB per month but sometimes uses up to 24 GB. There is also a one-off $20 setup fee on Plan A and no setup fee on Plan B. The student plans to stay on the plan for 12 months.
1. Calculate the 12-month total cost of each plan if the student uses 18 GB every month.
Read the worked answer
Plan A: Included data is 10 GB, so extra = 18 − 10 = 8 GB. Extra cost = 8 × $8 = $64 per month. Monthly total = $25 + $64 = $89. Over 12 months = $89 × 12 = $1,068. Add the $20 setup fee = $1,088.
Plan B: Included data is 30 GB, so 18 GB is within the allowance. No extra charge. Monthly total = $40. Over 12 months = $40 × 12 = $480.
Plan B is much cheaper at this usage level.
2. At what monthly data usage (in whole GB) does Plan A become cheaper than Plan B over 12 months, ignoring the setup fee? Show your reasoning.
Read the worked answer
Let extra GB on Plan A be x (where usage is above 10 GB). Plan A monthly cost = $25 + $8x. Plan B monthly cost = $40 as long as usage ≤ 30 GB.
Set $25 + $8x < $40, so $8x < $15, so x < 1.875. Since x must be a whole number, x = 0 or 1.
With x = 1, Plan A = $33 per month, which is less than $40. So Plan A is cheaper only when usage is 10 GB or 11 GB per month (x = 0 or 1). At 12 GB or more, Plan A costs $41 or more and Plan B is cheaper. Including the $20 setup fee, Plan A needs to save more than $20 over 12 months, which it does not at these small differences, so the setup fee pushes the break-even even further toward Plan B.
3. The student expects to sometimes use 24 GB. Which plan is the safer choice, and why?
Read the worked answer
At 24 GB, Plan A extra data = 24 − 10 = 14 GB, costing 14 × $8 = $112, so monthly cost = $25 + $112 = $137. Over 12 months that is $1,644 plus $20 setup = $1,664.
Plan B at 24 GB is within its 30 GB allowance, so monthly cost stays at $40, or $480 over 12 months.
Plan B is the safer choice because its higher included data (30 GB) absorbs the student's heavier months without extra charges. Plan A's low monthly fee is misleading once usage rises, because its extra-data rate is high. Plan B costs more up front each month but protects against bill shock.