A phone tariff models the total monthly cost, \(\pounds C\), for \(m\) minutes used beyond the free allowance as \(C=12+0.25m\), shown for some values of \(...
Question 1 Report
A phone tariff models the total monthly cost, \(\pounds C\), for \(m\) minutes used beyond the free allowance as \(C=12+0.25m\), shown for some values of \(m\) in the table, with one value missing, labelled \(p\).
| \(m\) | 0 | 20 | 40 | 60 |
|---|---|---|---|---|
| \(C\) | 12 | 17 | \(p\) | 27 |
- Find the value of \(p\). (1)
- A customer is charged \(\pounds33\) in total one month. Work out how many minutes beyond the allowance they used. (2)
Answer Details
The formula \(C=12+0.25m\) gives the monthly cost once the free minutes are used up, so it can be used forwards (substitute \(m\) to find \(C\)) or backwards (substitute a known \(C\) to find \(m\)).
(a) Substituting \(m=40\): \(C=12+0.25(40)=12+10=22\), so \(p=22\). [1 mark]
(b) Setting \(C=33\): \(12+0.25m=33\). Subtracting 12: \(0.25m=21\). Dividing by \(0.25\): \(m=84\) minutes beyond the allowance. [2 marks]
Because the cost rises by exactly \(\pounds0.25\) for every extra minute, each entry in the table rises by \(0.25\times20=5\) as \(m\) increases by 20, which is a useful check on the completed table: \(12, 17, 22, 27\) does indeed rise by 5 each time.
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