Question

the telephone company offers two billing plans for local calls. plan 1 charges $26 per month for unlimited calls and plan 2 charges $18 per month plus $0.04 per call. a. let x represent the number of monthly calls. the answer is (type an inequality). b. use an inequality to find the number of monthly calls for which plan 1 is more economical than plan 2. explain the meaning of the answer to part a.

Explanation:

Step1: Set up cost - functions

Let the cost of Plan 1 be $C_1 = 26$ (a flat - rate of $26$ per month). Let the cost of Plan 2 be $C_2=18 + 0.04x$, where $x$ is the number of monthly calls.

Step2: Set up the inequality

We want to find when Plan 1 is more economical than Plan 2, so we set up the inequality $C_1

Step3: Solve the inequality

Subtract 18 from both sides: $26−18<18 + 0.04x−18$, which simplifies to $8<0.04x$. Then divide both sides by 0.04: $\frac{8}{0.04}<\frac{0.04x}{0.04}$, so $x > 200$.

Answer:

$x>200$