SOLUTION: A shepherd had an unfortunate experience. He was looking after a number (n) of sheep when robbers overpowered him and stole 1/4 of his sheep. He managed to get 3 of the stolen shee

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Question 1035317: A shepherd had an unfortunate experience. He was looking after a number (n) of sheep when robbers overpowered him and stole 1/4 of his sheep. He managed to get 3 of the stolen sheep back. The robbers came back and stole 1/3 of the remaining sheep of which he again managed to get 2 back. The third time the robbers overpowered him, they stole 1/2 of the remaining sheep of which he once again managed to get 2 back . He then exactly had n/2 sheep left. Determine the value of n, showing all explanations
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
He initially had n sheep.
After 1/4 of his sheep was stolen, 3/4 of it remains. Getting back 3 means he has %283n%29%2F4+%2B+3 remaining.
The second time the robbers came, they stole 1/3 of %283n%29%2F4+%2B+3, thus %282%2F3%29%28%283n%29%2F4+%2B+3%29 was left. Having gotten 2 sheep back, the number of remaining sheep is %282%2F3%29%28%283n%29%2F4+%2B+3%29+%2B+2.
The third time the robbers came, they stole 1/2 of %282%2F3%29%28%283n%29%2F4+%2B+3%29+%2B+2, thus %281%2F2%29%28%282%2F3%29%28%283n%29%2F4+%2B+3%29+%2B+2%29 was left. Having gotten 2 sheep back, the number of remaining sheep is %281%2F2%29%28%282%2F3%29%28%283n%29%2F4+%2B+3%29+%2B+2%29%2B2.
The last quantity must be equal to n/2.
==> %281%2F2%29%28%282%2F3%29%28%283n%29%2F4+%2B+3%29+%2B+2%29%2B2++=n%2F2
==>%281%2F3%29%28%283n%29%2F4+%2B+3%29+%2B1+%2B2+=+n%2F2
==> n%2F4+%2B+1+%2B+3+=+n%2F2
==> 4+=+n%2F4 ==> highlight%28n+=+16%29.