Within ten days after receiving such list the auditor shall certify to the county commission of such county a list of the girls from the county in such home, stating the length of the term during the year each girl was in such home, as shown by the list certified by the superintendent, the amount due from the county on her account, and the total amount due on account of all. He shall credit on such statement whatever amount has been applied as a payment thereon from any funds of the county in the treasury. Such statement shall be a receipt to the county for any amount so credited, and shall be a bill for any amount still appearing to be due from the county. Unless the bill shall have been paid by the application of funds of the county in the state treasury, the county commission shall, at its next levy term, provide for the payment of the same, or such part as may not have been paid, and cause the amount to be paid into the state treasury. If the amount so due from any county be not paid in a reasonable time after such levy term, the auditor may in the name of the state, apply to the circuit court of the county for a mandamus to require the county commission to provide for and pay the same, or he may proceed in the name of the state by any other appropriate remedy to recover the same.