Mom left a plate of cookies out for everyone to eat. Claire was the first one home. She took 1/5 of the cookies on the plate plus 1/5 of a cookie. Jane came next and took 1/4 of the cookies that were left plus 1/4 of a cookie. Then came Noah, who ate 1/3 of the cookies that were left plus 1/3 of a cookie. Nelly got home last and took 1/2 of the cookies on the plate plus 1/2 of a cookie. Finally, Dad came in the room and took the last cookie. Everyone took a whole number of cookies; no one broke or crumbled the cookies on the plate. How many cookies did Mom leave on the plate? How many cookies did each person take?
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