On her plan, christina pays $5 just to place a call and $1 for each minute. When brenna makes an international call, she pays $1 to place the call and $5 for each minute. A call duration would cost exactly the same under both plans. What is the cost? What is the duration?

  $6 for a 1-minute call

Step-by-step explanation:

For duration "d" the costs of the plans are identical when ...

  5 +1d = 1 +5d

  4 = 4d . . . . . . . . add -1-1d to both sides

  1 = d  . . . . . . . . . divide by 4. Duration in minutes.

Then the cost for this 1-minute call is ...

  5 + 1·1 = 6 . . . . dollars

Each plan will charge $6 for a 1-minute call.

Step-by-step explanation:

Let x represent the call duration that would cost the same amount with either plans.

On her plan, christina pays $5 just to place a call and $1 for each minute. This means that the total cost of x minutes on this plan is

x + 5

When brenna makes an international call, she pays $1 to place the call and $5 for each minute. This means that the total cost of x minutes on this plan is

5x + 1

For both costs to be the same, the number of minutes would be

x + 5 = 5x + 1

5x - x = 5 - 1

4x = 4

x = 4/4 = 1

A call duration of 1 minute would cost exactly the same under both plans. The cost of the call would be

5 × 1 + 1 = $6

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