Question

the telephone company offers two billing plans for local calls. plan 1 charges $36 per month for unlimited calls and plan 2 charges $16 per month plus $0.04 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 x>500. (type an inequality.) b. explain the meaning of the answer to part a. choose the correct answer below. a. if the number of calls is less than 500, plan 1 is more economical. b. if the number of calls is more than 1300, plan 1 is more economical. c. if the number of calls is less than 1300, plan 1 is more economical. d. if the number of calls is more than 500, plan 1 is more economical.

Explanation:

Step1: Set up cost - function for each plan

Let $x$ be the number of monthly calls. Cost of Plan 1, $C_1 = 36$. Cost of Plan 2, $C_2=16 + 0.04x$.

Step2: Set up the inequality

We want to find when Plan 1 is more economical than Plan 2, so $C_1

Step3: Solve the inequality

Subtract 16 from both sides: $36−16<16 + 0.04x-16$, which simplifies to $20<0.04x$. Then divide both sides by 0.04: $\frac{20}{0.04}<\frac{0.04x}{0.04}$, and $x > 500$.

For part b:

Answer:

a. $x>500$
b. D. If the number of calls is more than 500, Plan 1 is more economical.