(A) With the approval of the department of education and workforce, the boards of education of any two or more joint vocational school districts may, by the adoption of identical resolutions by a majority of the members of each such board, propose that one new joint vocational school district be created by adding together all of the territory of each of the districts and dissolving such districts. A copy of each resolution shall be filed with the department for its approval or disapproval. The resolutions shall include a provision that the board of education of the new district shall be composed of the members from the same boards of education that composed the membership of the board of each of the districts to be dissolved, except that, if an even number of districts are to be dissolved, one additional member shall be added, who may be from any school district included in the territory of any of the districts to be dissolved as designated in the resolutions. The members of the new board shall have the same terms of office as they had under the respective plans of the districts adopting the resolutions, except that, if the new board has an additional member, the additional member shall have a term as specified in the resolutions. If the department approves the resolutions, the board of education of each district to be dissolved shall advertise a copy of the resolution in a newspaper of general circulation in its district once each week for two weeks, or as provided in section 7.16 of the Revised Code, immediately following the date the resolutions are approved by the department. The resolutions shall become effective on the first day of July next succeeding the sixtieth day following approval by the department unless prior to the expiration of such sixty-day period, qualified electors residing in one of the districts to be dissolved equal in number to a majority of the qualified electors of that district voting at the last general election file with the department a petition of remonstrance against creation of the proposed new district.