document.write( "Question 844041: There are five thieves, each loot a shop one after the other such that the first one takes 1/2 of the total no. of the Chocolates plus 1/2 of a Chocolate. Similarly 2nd, 3rd,4th and 5th also did the same. After the fifth one no. of Chocolates remained are 3. Initially how many Chocolates were there? \n" ); document.write( "

Algebra.Com's Answer #508518 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+c+\"$ = the initial number of chocolates
\n" ); document.write( "-----------------
\n" ); document.write( "The 1st thief takes $\"+c%2F2+%2B+1%2F2+\"$ , so
\n" ); document.write( "there are $\"+c%2F2+-+1%2F2+\"$ left
\n" ); document.write( "--------------------------
\n" ); document.write( "The 2nd thief takes $\"++c%2F4+-+1%2F4+%2B+1%2F2+\"$
\n" ); document.write( " $\"+c%2F4+%2B+1%2F4+\"$
\n" ); document.write( "There is $\"+c%2F2+-+1%2F2+-+c%2F4+-+1%2F4+\"$ left
\n" ); document.write( " $\"+c%2F4+-+3%2F4+\"$ left
\n" ); document.write( "---------------------------
\n" ); document.write( "The 3rd thief takes $\"+c%2F8+-+3%2F8+%2B+1%2F2+\"$
\n" ); document.write( " $\"+c%2F8+%2B+1%2F8+\"$
\n" ); document.write( "There is $\"+c%2F4+-+3%2F4+-+c%2F8+-+1%2F8+\"$ left
\n" ); document.write( " $\"+c%2F8+-+7%2F8+\"$ left
\n" ); document.write( "---------------------------
\n" ); document.write( "The 4th thief takes $\"+c%2F16+-+7%2F16+%2B+1%2F2+\"$
\n" ); document.write( " $\"+c%2F16+%2B+1%2F16+\"$
\n" ); document.write( "There is $\"+c%2F8+-+7%2F8+-+c%2F16+-+1%2F16+\"$ left
\n" ); document.write( " $\"+c%2F16+-+15%2F16+\"$ left
\n" ); document.write( "----------------------------
\n" ); document.write( "The 5th thief takes $\"+c%2F32+-+15%2F32+%2B+1%2F2+\"$
\n" ); document.write( " $\"+c%2F32+%2B+1%2F32+\"$
\n" ); document.write( "There is $\"+c%2F16+-+15%2F16+-+c%2F32+-+1%2F32+\"$ left
\n" ); document.write( " $\"+c%2F32+-+31%2F32+\"$ left
\n" ); document.write( "-----------------------------
\n" ); document.write( "given:
\n" ); document.write( " $\"+c%2F32+-+31%2F32+=+3+\"$
\n" ); document.write( " $\"+c+-+31+=+3%2A32+\"$
\n" ); document.write( " $\"+c+=+31+%2B+96+\"$
\n" ); document.write( " $\"+c+=+127+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( "There were 127 chocolates initially
\n" ); document.write( "check answer:
\n" ); document.write( "--------------------------------
\n" ); document.write( "1st thief takes $\"+127%2F2+%2B+1%2F2+=+64+\"$
\n" ); document.write( "There are $\"+127+-+64+=+63+\"$ left
\n" ); document.write( "--------------------------------
\n" ); document.write( "2nd thief takes $\"+63%2F2+%2B+1%2F2+=+32+\"$
\n" ); document.write( "There are $\"+63+-+32+=+31+\"$ left
\n" ); document.write( "--------------------------------
\n" ); document.write( "3rd thief takes $\"+31%2F2+%2B+1%2F2+=+16+\"$
\n" ); document.write( "There are $\"+31+-+16+=+15+\"$ left
\n" ); document.write( "--------------------------------
\n" ); document.write( "4th thief takes $\"+15%2F2+%2B+1%2F2+=+8+\"$
\n" ); document.write( "There are $\"+15+-+8+=+7+\"$ left
\n" ); document.write( "--------------------------------
\n" ); document.write( "5th thief takes $\"+7%2F2+%2B+1%2F2+=+4+\"$
\n" ); document.write( "There are $\"+7+-+4+=+3+\"$ left
\n" ); document.write( "OK\r
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