(a) General rule.--The county commissioners shall pay monthly to the Department of Human Services the:
(1) Amount expended by the department during the preceding month as assistance on behalf of:
(i) patients receiving public nursing home care in a county medical institution; and
(ii) children in foster family homes and child-caring institutions.
(2) Cost of administering the assistance, minus the amount of Federal money properly received by the Department of Human Services on account of expenditures increased or reduced by any amount by which the amount paid for any previous month differed from the amount which should have been paid for the previous month and by the proportionate share of refunds of assistance as provided in the act of June 13, 1967 (P.L.31, No.21), known as the Human Services Code.
(b) Certification.--The Department of Human Services shall certify to the county commissioners the amount to be paid by the county to the department under subsection (a).