Formula to Sum Charges Based on Dates for each Patient

Hello, i need your help. Please see Attached Excel worksheet.

I need a formula here that will look at the "charge worksheet" and if column "A" equals column A on the "Patients worksheet" and if the date of the charge corrosponding to the matching Patient falls between the "Admit" and "Discharge" dates, then sum those charges and return the summed value.

Thanks in advance.