A customer is comparing two monthly tariffs offered by a mobile phone company before signing a new contract. Tariff A costs £15 plus 4p per minute used, whi...
Question 1 Report
A customer is comparing two monthly tariffs offered by a mobile phone company before signing a new contract. Tariff A costs £15 plus 4p per minute used, while Tariff B costs £9 plus 7p per minute used. Form an inequality in \(m\), the number of minutes used, and solve it to find the number of minutes for which Tariff A costs less than Tariff B. (3)
Answer Details
This question compares two linear cost models by forming an inequality between them and solving for the range of usage where one is cheaper.
Tariff A costs less than Tariff B when:
\[15+0.04m \lt 9+0.07m\][1 mark]
Subtracting \(9\) and subtracting \(0.04m\) from both sides:
\[6 \lt 0.03m\][1 mark]
Dividing both sides by \(0.03\) (positive, so the inequality direction is unchanged):
\[m \gt 200\][1 mark]
Tariff A is cheaper than Tariff B when more than \(200\) minutes are used. This makes sense because Tariff A has a higher fixed fee but a lower cost per minute, so it only becomes the cheaper option once enough minutes are used to outweigh that higher starting cost.
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