Question

Customers of a phone company can choose between two service plans for long-distance calls. The first plan has a $26 monthly fee and charges an additional 0.11 for each minute of calls. The second plan has a $22 monthly fee and charges an additional 0.15 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answer 1

`\begin{equation*} 100\text{ minutes} \end{equation*}`

Step-by-step explanation

Let the number of minutes of calls be x.

For the first plan, the cost of the calls is $26 monthly plus an additional $0.11 for each minute of calls. This implies that the cost of calls for the first plan is:

`C_1=26+0.11x`

For the second plan, the cost of the calls is $22 monthly plus an additional $0.15 for each minute of calls. This implies that the cost of calls for the second plan is:

`C_2=22+0.15x`

When the costs of the two plans are equal, it implies that C1 is equal to C2:

`\begin{gathered} C_1=C_2 \\ \Rightarrow26+0.11x=22+0.15x \end{gathered}`

Now, we have to solve for x to find the number of minutes of calls for which the costs will be the same:

`\begin{gathered} 26+0.11x=22+0.15x \\ 26-22=0.15x-0.11x \\ 4=0.04x \\ x=(4)/(0.04) \\ x=100\text{ minutes} \end{gathered}`

That is the answer.