Should the majority of the qualified electors voting upon the question be in favor of such county, township, city or town hospital or tuberculosis camp, the county legislative delegation of such county shall proceed to appoint not more than seven nor less than three trustees to be chosen from citizens at large with reference to their fitness for such office, part of whom may be women, and all residents of the county, township, city or town, who shall constitute the trustees for such hospital or tuberculosis camp. The trustees shall hold their offices for two years or until their successors shall be appointed. Provided, that in Allendale County there may be appointed not more than nine trustees.