Lady Aisha Siddiqa (may Allah be pleased with her) said: We set out for Hajj with the Messenger of Allah (peace and blessings be upon him), and when we reached the place of Sarif, I began menstruating. Then, when the day of sacrifice came, I became pure, and the Messenger of Allah (peace and blessings be upon him) sent me for the Tawaf al-Ifadah. (When I returned,) beef was presented to me. I asked: What kind of meat is this? The reply was given that the Messenger of Allah (peace and blessings be upon him) has sacrificed a cow on behalf of his wives.
Hadith Referenceسنن دارمي / من كتاب المناسك / 1942
From this hadith, the permissibility of sacrificing a cow is established, which, like a camel, can be offered on behalf of seven individuals. Furthermore, it is proven that eating the meat of the sacrifice is Sunnah, and that purity (taharah) is a condition for performing tawaf. And Allah knows best.