Comparing two mobile plans with data overage
A student is choosing between two 12-month mobile plans.\n\nPlan A: $25 per month, includes 15 GB of data; excess data is charged at $10 per GB (charged per GB started, i.e. any part GB counts as a full GB).\n\nPlan B: $38 per month, includes 30 GB; excess data is $10 per GB (per GB started).\n\nOver the last few months the student's usage has been 14 GB, 22 GB, 27 GB and 31 GB. The student says, 'Plan A is cheaper because the monthly price is lower - I'll just watch my data.'
1. Calculate the total 12-month cost under each plan if the student's usage repeats this four-month pattern three times over the year.
Read the worked answer
Plan A: base cost 12 × $25 = $300.\nExcess data per four-month cycle:\n- 14 GB → 0 excess\n- 22 GB → 7 GB over → $70\n- 27 GB → 12 GB over → $120\n- 31 GB → 16 GB over → $160\nCycle excess = 70 + 120 + 160 = $350.\nThree cycles: 3 × 350 = $1,050.\nTotal Plan A = 300 + 1,050 = $1,350.\n\nPlan B: base cost 12 × $38 = $456.\nExcess per cycle:\n- 14 GB → 0\n- 22 GB → 0\n- 27 GB → 0\n- 31 GB → 1 GB over → $10\nCycle excess = $10; three cycles = $30.\nTotal Plan B = 456 + 30 = $486.\n\nPlan B is cheaper by $1,350 − $486 = $864.
2. Explain why the student's reasoning is flawed and state what usage assumption would make Plan A cheaper.
Read the worked answer
The student compared only the headline monthly price, ignoring that Plan A's small data allowance triggers heavy per-GB charges. The real cost depends on usage, not the sticker price.\n\nPlan A is cheaper only if excess charges stay low. Compare base costs: Plan B costs $13 more per month = $156 more per year. Plan A beats Plan B only if its annual excess charges total less than $156, i.e. fewer than about 15–16 excess GB across the whole year.\n\nGiven the student regularly uses 22–31 GB, Plan A will almost certainly cost more. The judgement call is to estimate typical usage first, then compare total costs - not monthly prices.