Question

customers of a phone company can choose between two service plans for long distance calls. the first plan has a $22 monthly fee and charges an additional $0.13 for each minute of calls. the second plan has a $9 monthly fee and charges an additional $0.18 for each minute of calls. for how many minutes of calls will the costs of the two plans be equal?

Explanation:

Step1: Define variables & cost equations

Let $x$ = number of call minutes.
Cost of Plan 1: $C_1 = 22 + 0.13x$
Cost of Plan 2: $C_2 = 9 + 0.18x$

Step2: Set costs equal to each other

$$22 + 0.13x = 9 + 0.18x$$

Step3: Isolate $x$ terms

$$22 - 9 = 0.18x - 0.13x$$
$$13 = 0.05x$$

Step4: Solve for $x$

$$x = \frac{13}{0.05} = 260$$

Answer:

260 minutes