Whenever the education of a child becomes the state's direct responsibility for any reason, the commissioner shall pay to the state agency responsible for the child, or as may be otherwise directed in the general appropriations act, an amount equal to the state funds, plus the local funds that would otherwise be expended on the child had the child not been placed under state care. The total amount of the payments shall be deducted by the commissioner from the total state payments that would otherwise be made under this part to the LEA that would be responsible for the child's education had the child not been placed under the state's direct responsibility.