SOLUTION: Once again I need help with a math problem. janet From a box of bananas person "A" eats one third of the contents. A while later person "B" eats one third of the remaining bananas

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Question 201439This question is from textbook Mathematics For Technical trades
: Once again I need help with a math problem. janet
From a box of bananas person "A" eats one third of the contents. A while later person "B" eats one third of the remaining bananas. A while later person "C" eats one third of the remaining bananas. When person "C" finished eating there were 8 bananas left in the box. How many bananas were in the box originally? This question is from textbook Mathematics For Technical trades

Found 2 solutions by solver91311, jsmallt9:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

If "C" had one-third of what was left after "B" was done, then 8 must be two-thirds of what was left after "B" was done, so the number left after "B" was done is 8 divided by or . Likewise, the number left after "A" was done is . And finally, the number that was there at the start was .

John

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
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.

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. 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 %282%2F3%29%2Ax bananas left.
When "B" starts there are %282%2F3%29%2Ax bananas. When "B" is done there is 2/3 of %282%2F3%29%2Ax or %282%2F3%29%2A%282%2F3%29%2Ax bananas left. Multiplying we get %284%2F9%29%2Ax.
When "C" starts there are %284%2F9%29%2Ax bananas. When "C" is done there is 2/3 of %284%2F9%29%2Ax or %282%2F3%29%2A%284%2F9%29%2Ax left. Multiplying we get %288%2F27%29%2Ax.
We are told that after "C" is done that there are 8 bananas. So
%288%2F27%29%2Ax=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.