A cellular telephone company has two plans. plan a charges 11.00 a mouth and 0.21 per minute. plan b charges 20.00 a mouth and 0.10 per minute. after how much time, to the nearest minute, will the cost of the plan a be equal to cost of plan b

I think you mean that the plans charge $11.00 per month and $20.00 per month and not per mouth.

Let m = number of minutes

Plan A:

cost = fixed charge + per minute charge

cost = 11 + 0.21m

Plan B:

cost = fixed charge + per minute charge

cost = 20 + 0.10m

You want the plans to cost the same, so set the costs equal.

11 + 0.21m = 20 + 0.10m

Subtract 11 from both sides:

0.21m = 9 + 0.10m

Subtract 0.10m from both sides:

0.11m = 9

Divide both sides by 0.11:

m = 9/0.11 = 81.81

Round 81.81 to 82.

Answer: 82 minutes