Final answer:
The spleen contains red pulp and white pulp. The red pulp filters out old or damaged red blood cells, while the white pulp is involved in mounting adaptive immune responses.
Step-by-step explanation:
The lymphatic organ that contains both red pulp and white pulp is the spleen. The spleen performs multiple functions within the lymphatic system, including filtering blood, removing damaged red blood cells, and combatting infections. The red pulp of the spleen consists of reticular fibers, free macrophages, and all of the other cells typical of the blood, including some lymphocytes. Its primary function is to filter out old or damaged red blood cells. In contrast, the white pulp resembles the lymphoid follicles of the lymph nodes and is rich in lymphocytes, specifically B cells and T cells. It functions as a site where adaptive immune responses are mounted against antigen-coated bacteria.