SOLUTION: the owner of a peach orchard hired 3 watchmen to watch his orchard. A brigand gained access to the orchard, however, and purloined some peaches. He met each of the three watchmen o

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Question 759059: the owner of a peach orchard hired 3 watchmen to watch his orchard. A brigand gained access to the orchard, however, and purloined some peaches. He met each of the three watchmen on his way out. To each, he gave one-half of the peaches he had, plus 2 more besides. He got out of the orchard with only one peach. How many peaches did he pick and attempt to steal.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Manage this stepwise and give a variable to the amount of stolen peaches.

Let p = count of stolen peaches, p for purloined.

Step 1:
After giving the described quantities to the first watchman, the brigand still had p-%28%281%2F2%29p-2%29 peaches.

Step 2:
Some peaches he gave to a second watchman. The brigand now has
%28p-%28%281%2F2%29p-2%29%29-%28%281%2F2%29%28p-%28%281%2F2%29p-2%29%29-2%29 peaches.

Step 3:
He must do the same thing for the last watchman. He has now,


The objective is solve that for p.

SOME DISCUSSION IS USEFUL. At each step, you should simplify the expression as much as possible; and use the basic pattern established at step 1, to build the expression for the next step. This should reduce the difficulty of trying to read through the compositions in the symbolic form I have shown in step 3.