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Three students were doing their homework together.?
Three students were doing their homework together. As a treat, one mom offered to bake some cookies. While waiting for them to cool, all three students feel asleep. After a while, student 1 woke up, ate her equal share of cookies, and went back to sleep. A little while later, student 2 woke up, ate what she thought was her equal share, and fell asleep again. Then student 3 woke up, ate what she thought was her equal share, and went back to sleep. Later, all three kids woke up and discovered that the number of cookies left could be divided among themselves equally if they gave on to the mother that baked them. How many cookies were baked originally? Give the smallest possible amount.
My method was
x - (1/3)x - (1/3)(2/3)x - (1/3)(4/9)x = (8/27)x
As they gave one cookie to the mother, it would be
(8/27)x - 1
As the remaining cookies can be divided among themselves equally now, it would be
(8/81)x - (1/3)
However, the issue I am having it what to set the amount of cookies they each receive. If I set it equal to 1, I would get 13.5 total cookies baked. Is there a way to get a whole amount of total cookies baked?
Thanks.
I kept on change the value of cookies received by each student. Upon reaching 5, I discovered that the total number of cookies baked would be 54, a whole number. Is there a more mathematical / logical way to get the answer instead of plug-in check?
