Question

the telephone company offers two billing plans for local calls. plan 1 charges $33 per month for unlimited calls and plan 2 charges $16 per month plus 4 cents per call. use an inequality to find the number of monthly calls for which plan 1 is more economical than plan 2. plan 1 is more economical than plan 2 if more than calls are made each month.

Explanation:

Step1: Set up cost - functions

Let $x$ be the number of monthly calls. The cost of Plan 1, $C_1 = 33$. 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 for $x$

Subtract 16 from both sides: $33−16<16 + 0.04x−16$, which simplifies to $17<0.04x$.
Then divide both sides by 0.04: $\frac{17}{0.04}<\frac{0.04x}{0.04}$.
Since $\frac{17}{0.04}=425$, we have $x > 425$.

Answer:

425