Step 1 :Megan's regular pay is calculated by multiplying her regular hourly rate by the number of regular hours she works. In this case, it is \(19 \times 40 = 760\) dollars.
Step 2 :Megan's overtime pay is calculated by multiplying the number of overtime hours she works by her overtime rate. The overtime rate is 1.5 times her regular hourly rate. In this case, it is \(3 \times 28.5 = 85.5\) dollars.
Step 3 :Megan's total gross pay for the week is the sum of her regular pay and her overtime pay. In this case, it is \(760 + 85.5 = 845.5\) dollars.
Step 4 :Final Answer: Megan's gross pay for the week was \(\boxed{845.5}\) dollars.