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FUN FUN FUN!!! Math and Holiday Pastries!!! Yum!!! Please help!!!?

During the night, Papa got up and ate one-third of the pastries. He then (separate from the 1/3) gave one pastry to his dog. Ed was the next to get up. He planned to eat 1/4 of the pastries, but when he sepatated them into 4 piles, he found there were 3 pastries left over. He decided to feed those pastries to the dog and ate the original planned 1/4 of the remaining pastries. Lisa ate 1/3 of the remaining pastries. She then gave 2 pastries to the dog. Judy ate 8 pastries and then gave 1/8 of the remaining to the dog. The next morning Mama noticed there were only 14 pastries left. She ate 2, gave 2 to the dog, and then split the remaining pastries evenly for her whole family (5 people in all: mama, papa, Ed, Judy, Lisa), including herself, to have for breakfast. How many pastries did the family bake originally and how many did each person consume? Please explain and show your work! Thanks!

Man this one be one fat family. Anyway, this problem is based off an old puzzle from Lewis Carol. It’s sometimes best with these to work them backwards. But I’m going to do it forwards.

Let “P” be the original number of pastries. Papa took one third away and then give one to his dog. This leaves
P – (1/3)P – 1 = (2/3)P – 1

Ed essentially removed 3, then took 1/4 of what remained. So this leaves ((2/3)P – 4)(3/4) = P/2 – 3.

Lisa ate 1/3 of this, then gave 2 to the dog. So what’s left is 2/3 of the last value, minus 2:
(P/2 – 3)(2/3) – 2 = P/3 – 2 – 2 = P/3 – 4.

Judy ate 8 then gave 1/8 to the dog, so this leaves
(P/3 – 4 – 8)(7/8) = (P/3 – 12)(7/8) = 7P/24 – 21/2. We’re told this is equal to 14, so
7P/24 – 21/2 = 14
7P/12 – 21 = 28
7P/12 = 49
P/12 = 7
P = 84.

First Papa ate 1/3 of this, or 28. At the end he got (14-2-2 = 10/5 = 2) two more from Mama, for a total of 30.

Ed ate ((2/3)P – 4)(1/4) = 13, plus 2 more at the end to make 15.

Judy ate 8 plus the 2 from Mama, for a total of 10.

Lisa ate (P/2 – 3)(1/3) = 13, plus 2 at the end, for a total of 15.

Mama had 2 when nobody was looking, then had 2 more at the end for a total of 4.

The dog got 1 + 3 + 2 + (1/8)(P/3 – 12) + 2 = 10.

You can verify that the total adds up to 84.

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