From the sums appropriated therefor and the allotments available under section 702(c) of this title, the Secretary shall make payments as provided by section 6503(a) of title 31 to each State provided such an allotment under section 702(c) of this title, for each quarter, of an amount equal to four-sevenths of the total of the sums expended by the State during such quarter in carrying out the provisions of this subchapter.