SOLUTION: 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 a

Algebra ->  Inequalities -> SOLUTION: 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 a      Log On


   

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?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the initial number of chocolates
-----------------
The 1st thief takes +c%2F2+%2B+1%2F2+, so
there are +c%2F2+-+1%2F2+ left
--------------------------
The 2nd thief takes ++c%2F4+-+1%2F4+%2B+1%2F2+
+c%2F4+%2B+1%2F4+
There is +c%2F2+-+1%2F2+-+c%2F4+-+1%2F4+ left
+c%2F4+-+3%2F4+ left
---------------------------
The 3rd thief takes +c%2F8+-+3%2F8+%2B+1%2F2+
+c%2F8+%2B+1%2F8+
There is +c%2F4+-+3%2F4+-+c%2F8+-+1%2F8+ left
+c%2F8+-+7%2F8+ left
---------------------------
The 4th thief takes +c%2F16+-+7%2F16+%2B+1%2F2+
+c%2F16+%2B+1%2F16+
There is +c%2F8+-+7%2F8+-+c%2F16+-+1%2F16+ left
+c%2F16+-+15%2F16+ left
----------------------------
The 5th thief takes +c%2F32+-+15%2F32+%2B+1%2F2+
+c%2F32+%2B+1%2F32+
There is +c%2F16+-+15%2F16+-+c%2F32+-+1%2F32+ left
+c%2F32+-+31%2F32+ left
-----------------------------
given:
+c%2F32+-+31%2F32+=+3+
+c+-+31+=+3%2A32+
+c+=+31+%2B+96+
+c+=+127+
------------------------------
There were 127 chocolates initially
check answer:
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1st thief takes +127%2F2+%2B+1%2F2+=+64+
There are +127+-+64+=+63+ left
--------------------------------
2nd thief takes +63%2F2+%2B+1%2F2+=+32+
There are +63+-+32+=+31+ left
--------------------------------
3rd thief takes +31%2F2+%2B+1%2F2+=+16+
There are +31+-+16+=+15+ left
--------------------------------
4th thief takes +15%2F2+%2B+1%2F2+=+8+
There are +15+-+8+=+7+ left
--------------------------------
5th thief takes +7%2F2+%2B+1%2F2+=+4+
There are +7+-+4+=+3+ left
OK