Math Problem Statement
A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $7.40 and then an additional 5 cents per minute of use. In Plan B, there is no monthly fee, but the customer pays 7 cents per minute of use. For what amounts of monthly phone use will Plan A cost more than Plan B? Use m for the number of minutes of phone use in a month, and solve your inequality for m.
Solution
We are tasked with determining when Plan A costs more than Plan B based on the number of minutes used in a month.
Step 1: Define the cost expressions for each plan.
- Plan A: The customer pays a fixed monthly fee of $7.40 plus 5 cents per minute. The total cost for Plan A is:
- Plan B: The customer pays no monthly fee but is charged 7 cents per minute. The total cost for Plan B is:
Step 2: Set up the inequality.
We want to find when Plan A costs more than Plan B, so we set up the inequality:
Step 3: Solve the inequality.
First, subtract from both sides to isolate on one side: Simplifying the right-hand side:
Now, divide both sides by to solve for :
Perform the division:
Conclusion:
Plan A will cost more than Plan B when the number of minutes used in a month is less than 370. Therefore, Plan A is more expensive for any usage less than 370 minutes.
Would you like further details or have any questions?
Here are 5 related questions you might explore:
- At how many minutes does Plan A and Plan B cost the same?
- What is the total cost for 200 minutes of use in Plan A?
- What is the total cost for 450 minutes of use in Plan B?
- How much will a user save by switching from Plan A to Plan B if they use 350 minutes?
- For what number of minutes would both plans exceed $40 in total cost?
Tip: When comparing plans with a fixed fee and per-minute charge, setting up inequalities is a useful way to determine the break-even point.
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Linear Equations
Formulas
Cost of Plan A = 7.40 + 0.05m
Cost of Plan B = 0.07m
Inequality: 7.40 + 0.05m > 0.07m
Theorems
Basic principles of inequality solving
Suitable Grade Level
Grades 7-9
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