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Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $13 monthly fee and charges an additional $0.17 for each minute of calls. The second plan has a $23 monthly fee and charges an additional $0.13 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

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luisejr77

Answer:

With 250 minutes of calls the cost of the two plans is the same

Step-by-step explanation:

We must write an equation to represent the cost of each call plan.

For the first plan

Monthly fee

 $ 13

Cost per minute

 $ 0.17

If we call x the number of call minutes then the equation representing the cost c for this plan is:

[tex]c = 13 + 0.17x[/tex]

For the second plan

monthly fee

$ 23

Cost per minute

$ 0.13

If we call x the number of call minutes then the equation representing the cost c for this plan is:

[tex]c = 23 + 0.13x[/tex]

To know when the cost of both plans are equal, we equate the two equations and solve for x.

[tex]13 + 0.17x = 23 + 0.13x\\\\0.17x -0.13x = 23-13\\\\0.04x = 10[/tex]

[tex]x = \frac{10}{0.04}[/tex]

[tex]x = 250\ minutes[/tex]

With 250 minutes of calls the cost of the two plans is the same: $55.5