Question

the telephone company offers two billing plans for local calls. plan 1 charges $20 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: Define cost functions

Let $C_1 = 20$ be the cost of Plan 1 per month and $C_2=18 + 0.04x$ be the cost of Plan 2 per month, 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 $C_1

Step3: Solve the inequality

Subtract 18 from both sides: $20-18<18 + 0.04x-18$, which simplifies to $2<0.04x$. Then divide both sides by 0.04: $\frac{2}{0.04}<\frac{0.04x}{0.04}$, so $x > 50$.

Answer:

a. $20<18 + 0.04x$
b. The inequality $20<18 + 0.04x$ means that when the number of monthly calls $x$ is greater than 50, Plan 1 is more economical than Plan 2. The solution of the inequality is $x>50$, which indicates that if the number of monthly calls is more than 50, Plan 1 is the better - value option.