Customers of a phone company can choose between two service plans for long distance calls. The first plan has no monthly fee but charges for each minute of calls. The second plan has a monthly fee and charges an additional for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Assume that the price of each minute in the first plan is $c and that the second plan charges a flat rate of $P and a charge of additional $d for every minute.

Step-by-step explanation

Assume that the price of each minute in the first plan is $c and that the second plan charges a flat rate of $P and a charge of additional $d for every minute.

Thus, the monthly cost of a customer who consumes x minutes in each plan is:

For the first plan: [tex]cx[/tex]

and for the second plan: [tex]P + dx[/tex]

Considering that the monthly costs must be the same in each plan, you have to:

[tex]cx = P + dx\\ transposing terms

\\cx - dx = P\\ applying common factor

\\(c -d)x = P\\ dividing by [tex]c - d[/tex]

\\x= P/(c -d)[/tex].

For example if [tex]c = $2; d = $1 y P = $10[/tex], Then the number of minutes would be, [tex]x=10[/tex] and the total cost for each plan would be [tex]$20[/tex]