Such expenses shall be paid on the warrant of the county board of education. The superintendent’s claim for services and expenses shall be presented in the form of an itemized account against the county board of education, verified by affidavit to the effect that said account is just and true, that the service therein named was honestly and faithfully rendered and that the sum therein claimed is rightfully due and remains unpaid. When such account shall have been duly audited and approved by the county board of education, it shall be filed with the county treasurer, who shall pay the same ratably out of the funds apportioned to the several school districts in proportion to the average number of children attending the free public schools in each school district.