Question

the telephone company offers two billing plans for local calls. plan 1 charges $39 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
(type an inequality.)

Explanation:

Step1: Set up cost - functions

Let $x$ be the number of monthly calls. The cost of Plan 1, $C_1 = 39$. The 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: $39−16<16 + 0.04x-16$, which simplifies to $23<0.04x$. Then divide both sides by 0.04: $\frac{23}{0.04}<\frac{0.04x}{0.04}$, so $x > 575$.

Answer:

a. $39<16 + 0.04x$ (or $x>575$)
b. The meaning of the answer $x > 575$ is that when the number of monthly local calls is greater than 575, Plan 1 is more economical (costs less) than Plan 2.