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Two monthly cell phone plans have costs, in dollars, modeled by the following expressions. The variable \(m\) is the number of gigabytes of data used.
Plan 1: \(10+2m\)
Plan 2: \(4m\)
a) Describe the base fee and cost per gigabyte for each plan.
b) Let \(E\) represent the amount saved by choosing Plan 1 instead of Plan 2. Write and simplify an expression for \(E\).
c) Find \(E\) when \(m=3\) and when \(m=7\). Interpret each result.
Hints
- In a cost expression, what does a constant term represent? What does the coefficient of \(m\) represent?
- Savings equal the cost not chosen minus the cost chosen.
- Use parentheses when subtracting an entire cost expression.
- What does a negative savings value mean?
Solution
1. Plan 1 has a base fee of \(\$10\) and costs \(\$2\) per gigabyte. Plan 2 has no base fee and costs \(\$4\) per gigabyte.
2. Savings from choosing Plan 1 are Plan 2 cost minus Plan 1 cost: \(E=4m-(10+2m)\).
3. Simplify: \(E=4m-10-2m=2m-10\).
4. When \(m=3\), \(E=2\cdot3-10=-4\). The negative value means Plan 1 costs \(\$4\) more.
5. When \(m=7\), \(E=2\cdot7-10=4\). The positive value means Plan 1 saves \(\$4\).
Answer
a) Plan 1: \(\$10\) base fee and \(\$2\) per gigabyte. Plan 2: no base fee and \(\$4\) per gigabyte.
b) \(E=2m-10\)
c) For \(m=3\), \(E=-4\), so Plan 1 costs \(\$4\) more. For \(m=7\), \(E=4\), so Plan 1 saves \(\$4\).
