```Question 201439
This problem is a lot easier if you think about what fraction of the bananas each person left for the next person (instead of of fraction of the bananas each person ate). If someone eats 1/3 of the bananas, what fraction of the bananas is left afterwards? I hope it is clear that the fraction of bananas that is left is 2/3.<p>We also need to know how to calculate a fraction of some number. Whenever you see "a fraction of some number" (like "2/3 of the bananas") we will always multiply the fraction times the number. In our case we will multiply 2/3 times the number of bananas.<Now we are ready to start a solution to your problem.
Let x = the original number of bananas.
When "A" starts there are "x" bananas. When "A" is done there is 2/3 of x or {{{(2/3)*x}}} bananas left.
When "B" starts there are {{{(2/3)*x}}} bananas. When "B" is done there is 2/3 of {{{(2/3)*x}}} or {{{(2/3)*(2/3)*x}}} bananas left. Multiplying we get {{{(4/9)*x}}}.
When "C" starts there are {{{(4/9)*x}}} bananas. When "C" is done there is 2/3 of {{{(4/9)*x}}} or {{{(2/3)*(4/9)*x}}} left. Multiplying we get {{{(8/27)*x}}}.
We are told that after "C" is done that there are 8 bananas. So
{{{(8/27)*x=8}}}
We can solve for x by multiplying both sides by 27/8 (or by dividing both sides by 8/27). This gives x = 27. Since x represents the original number of bananas and since that is what we were asked to find, 27 is the answer.

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