Comparing Two Mobile Phone Plans
A student compares two prepaid mobile plans for a year. Plan X charges a flat 15 BAM per month and includes 5 GB of data; extra data costs 2 BAM per GB. Plan Y charges 8 BAM per month with 2 GB included; extra data costs 3 BAM per GB. The student estimates using 4 GB per month on average but sometimes 6 GB. There is also a one-time SIM activation fee: Plan X charges 10 BAM, Plan Y charges 0 BAM. The student has saved 200 BAM for the year and wants to know which plan is safer if monthly use varies.
1. Calculate the annual cost of each plan at an average use of 4 GB per month, including the activation fee.
Read the worked answer
Plan X: 15 BAM/month covers 5 GB, so 4 GB needs no extra data. Monthly cost = 15 BAM. Annual = 15 × 12 = 180 BAM. Add activation 10 BAM → 190 BAM.
Plan Y: 8 BAM/month covers only 2 GB, so 4 GB means 2 GB extra at 3 BAM = 6 BAM. Monthly = 8 + 6 = 14 BAM. Annual = 14 × 12 = 168 BAM. Activation 0 BAM → 168 BAM.
Comparison: At 4 GB per month, Plan Y is cheaper by 190 − 168 = 22 BAM per year. Both fit within the 200 BAM savings, so cost alone favours Y at this usage level.
2. The student sometimes uses 6 GB in a month. Determine which plan is safer against the 200 BAM budget when use varies.
Read the worked answer
Plan X at 6 GB: 1 GB extra at 2 BAM = 2 BAM. Monthly = 17 BAM. If every month were 6 GB: 17 × 12 = 204 BAM + 10 = 214 BAM, which exceeds 200 BAM. But at average 4 GB the annual cost is 190 BAM, so X stays inside budget unless use is consistently high.
Plan Y at 6 GB: 4 GB extra at 3 BAM = 12 BAM. Monthly = 8 + 12 = 20 BAM. If every month were 6 GB: 20 × 12 = 240 BAM, well over 200 BAM.
Safer choice: Plan X. Its flat fee includes more data, so extra-data charges start later and grow more slowly (2 BAM/GB vs 3 BAM/GB). Plan Y is cheaper only if use stays near 4 GB; a few heavy months push it past the budget. The activation fee of 10 BAM is a one-time cost and does not change this conclusion.