From the sums appropriated therefor and the allotment under this subpart, subject to the conditions set forth in this section, the Secretary shall from time to time pay to each State that has a plan developed in accordance with section 622 of this title an amount equal to 75 percent of the total sum expended under the plan (including the cost of administration of the plan) in meeting the costs of State, district, county, or other local child welfare services.