Pam says she will charge 125 plus 15 an hour to paint a house. michelle will charge $50 plus $20 per hour to paint a house. after how many hours will their cost be the same

Let us assume the number of hours after which the cost of Pam and Michelle will be same = x
Now let us concentrate on the information's already given in the problem.
Fixed charge taken by Pam = $125
Charge per hour taken by Pam = $15
Fixed charge taken by Michelle = $50
Charge per hour taken by Michelle = $20
Then
125 + 15x = 50 + 20x
20x - 15x = 125 - 50
5x = 75
x = 75/5
  = 15
So after 15 hours the charge taken by Pam and Michelle will be the same. I hope the procedure for doing this type of problem is clear to you.