A variable-magnification projection optical system substantially consists of a negative first lens group that is disposed at the most enlargement-side position and is fixed during magnification change, a positive last lens group that is disposed at the most reduction-side position and is fixed during magnification change, and a plurality of lens groups that are disposed between the first lens group and last lens group and are moved during magnification change. The lens groups that are moved during magnification change substantially consist of three lens groups, wherein the most enlargement-side lens group is a negative lens group. Predetermined conditional expressions relating to a back focus of the entire system on the reduction side at the wide-angle end, a focal length of the entire system at the wide-angle end, a focal length of the last lens group, and a focal length of the first lens group are satisfied.