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Jayant went to the hardware store to buy some needed supplies. He spent half of what he had plus \$2.00 in the first store; half of what he had left plus \$1.00 in the second store; half of what he had left plus \$1.00 in the third store; and in the last store half of all he had. Three dollars were left over.

posted May 4, 2015

I think he has started with 64
On first store=64/2 - 2=32-2=30
On second store = 30/2 - 1 =15-1= 14
On third store= 14/2-1=7-1=6
On last store= 6/2=3
So finally he remains with 3 dollars

64 is the correct answer but algebraic reach is as under
he spends x/2 +2 in the first store and is left with x/2-2 dollars
he spends half of this +1 means x/4-1+1 in the second store and is left with x/4-2
he spends half of this +1 means x/8-1+1 in the third store and is left with x/8-2
he spends half of this means x/16-1 in the last store and is left with x/16-1 which is 3 dollars giving x=64

Let us check
out of 64 spent in first store 34 left with 30
out of 30 spent in second store 16 left with 14
out of 14 spent in third store 8 left with 6
spends 3 in the last store and is left with 3

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