Zara is looking for a new mobile phone plan. She has found two plans that suit her needs and wants to work out which plan is cheaper depending on how many minutes she uses.
Plan \(\text{A}\): $20 per month fixed charge plus $0.10 per minute
Plan \(\text{B}\): $0.30 per minute, no fixed charge
Let \(C\) = total monthly cost in dollars, and \(m\) = number of minutes used.
- Plan \(\text{B}\) can be modelled by the equation \(C=0.30m\).
- Write an equation for the monthly cost of Plan \(\text{A}\). (1 mark)
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- The graph of Plan \(\text{B}\) is provided on the grid below. Use the equation from (a) to add the graph of Plan \(\text{A}\) to the grid. (2 marks)
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- For how many minutes per month do both plans cost the same amount? (1 mark)
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- Zara uses an average of 140 minutes per month.
- Which plan she should choose and how much does she save compared to the other plan. (1 mark)
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a. \(\text{Plan A: }C=20+0.10m\)
b.
c. \(100\ \text{minutes}\)
d. \(\text{Plan A, cheaper by } \$8\)
a. \(\text{Plan A: }\ C=20+0.10m\)
b. \(\text{Table of values}\)
\(\begin{array}{|c|c|c|c|c|c|} \hline m & 0 & 50 & 100 & 150 & 200 \\ \hline \text{Plan A} & 20 & 25 & 30 & 35 & 40 \\ \hline \end{array}\)
c. \(\text{From the graph, the lines intersect at }\ m=100.\)
\(\therefore\ \text{Both plans cost the same at } 100\ \text{minutes}\)
d. \(\text{Plan A: }\ C=20+0.10\times140=\$34\)
\(\text{Plan B: }\ C=0.30\times140=\$42\)
\(\text{Difference} = 42-34=\$8\)
\(\therefore\ \text{Zara should choose Plan A, which is \$8 cheaper than Plan B.}\)