Bridget needs an actor. actor a is offering her services for an initial $250 in addition
to $50 per day. actor b is offering her services for an initial $200 in addition to $60
per day. when will the two actors charge the same amount of money?

$250 + 50x = $200 + 60x

Get like terms on the same side using subtraction
250 -200 + 50x = 60x
50 + 50x - 50x = 60x -50x
50 = 10x     now divide by 10 and get 5 days.

Let's check

Day 1  Actor A is $250 + 50 = $300  Actor B = $200 + 60 = $260
Day 2 Actor A is $250 + 100 = $350  Actor B = $200 + 120 = $320
Day 3 Actor A is $250 + 150 = $400   Actor B = $200 + 180 = $380
Day 4 Actor A  is $250 + 200 = $450   Actor B = $200 + 240 = $440
Day 5  Actor A is $250 + 250 = $500    Actor B = $200 + 300 = $500