In each county subject to this subsection, the compensation of the members of any board of equalization and adjustments, as provided in Section 40-3-7, shall be paid 22 1/2 percent by the state, 38 3/4 percent by the county and 38 3/4 percent by the largest municipality in the county.

The county board of equalization in any county may further provide for an inventory of all property in the county, which inventory shall be under the supervision and control of the board. The state, county, and governing body of all municipalities in the county and all boards of education or boards of school commissioners are hereby authorized to contribute so much of the cost of the inventory as may be approved by the various governing bodies in the county and the board of education or boards of school commissioners. In the event the state elects to contribute to the cost of the inventory, the amount to be contributed shall be approved by the state Commissioner of Revenue and the Governor.

In all counties having a population of 140,000 or more according to the last or any subsequent federal census, it shall be the duty of the county commission or other like governing bodies of such counties in this state, to furnish and supply the county boards of equalization with adequate office space, necessary furniture and equipment, all necessary books, maps, stationery, and printed blanks, and transportation or reasonable compensation for transportation expense actually incurred in performance of official duties.