A phone company compares two tariffs. Tariff A costs \(\pounds(10+2d)\) and Tariff B costs \(\pounds(20+d)\), for \(d\) gigabytes of data used, shown for so...
Question 1 Report
A phone company compares two tariffs. Tariff A costs \(\pounds(10+2d)\) and Tariff B costs \(\pounds(20+d)\), for \(d\) gigabytes of data used, shown for some values of \(d\) in the table below, with one value missing.
| Data (GB) | Tariff A cost | Tariff B cost |
|---|---|---|
| 5 | 20 | 25 |
| 10 | ? | 30 |
| 15 | 40 | 35 |
- Complete the table for Tariff A when \(d=10\). (1)
- State, with a reason, which tariff is cheaper when \(d=15\). (2)
Answer Details
Substituting \(d=10\) into Tariff A's formula completes the table; comparing the two costs at a single value of \(d\) then decides which tariff is cheaper there.
(a) \(10+2(10) = 30\). The completed table is:
| Data (GB) | Tariff A cost | Tariff B cost |
|---|---|---|
| 5 | 20 | 25 |
| 10 | 30 | 30 |
| 15 | 40 | 35 |
[1 mark]
(b) At \(d=15\), Tariff A costs \(\pounds40\) and Tariff B costs \(\pounds35\). Since \(\pounds35\lt\pounds40\), Tariff B is cheaper at this level of data use. [2 marks]
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