Electrolytic cartridges for, systems for, and methods of electrolyzing a brine solution of water and an alkali salt to produce acidic electrolyzed water and alkaline electrolyzed water are provided. The system includes an internal chamber for receiving the brine solution and at least two electrolytic cartridges immersed in a brine bath. Each electrolytic cartridge includes an electrode, an ion selective membrane disposed on a side of the electrode so as to define a space adjacent to at least a portion of the electrode, a permeable insert covering the ion selective membrane on a side opposite the space, and a bonding plate disposed on the permeable insert on a side opposite the side facing the ion selective membrane. The methods recycle at least a portion of alkaline electrolyzed water into the feed of a cartridge having a positively charged electrode.