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Question

The telephone company offers two billing plans for local calls. Plan 1 charges $36 per month for unlimited calls and Plan 2 charges $13 per month plus $0.05 per call a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2 b. Explain the meaning of the answer to part a. a. Let x represent the number of monthly calls. The answer is (Type an inequality.)

Answer

Plan 1 becomes more cost-effective than Plan 2 after making 460 phone calls. Step-by-step explanation: Plan 1: 36x + 0y Plan 2: 13x + 0.05y To determine when Plan 1 becomes more economical than Plan 2, we need to compare the cost of both plans after a certain number of calls. We know that Plan 1 has a fixed cost of 36x, while Plan 2 has a fixed cost of 13x plus a variable cost of 0.05y. We can set up the inequality 36x < 13x + 0.05y to compare the costs of the two plans. Simplifying this inequality, we get 23x < 0.05y. To determine the minimum number of calls needed for Plan 1 to be more economical than Plan 2, we can solve for y. Dividing both sides of the inequality by 0.05x, we get: 23/0.05x < y Simplifying this expression, we get: 460x < y Therefore, after making 460 phone calls, Plan 1 becomes more cost-effective than Plan 2.