Question 703332: Ann, Betty, and Carol dedice to do some fancy swapping of their money. First, Ann doubles Betty's money and doubles Carol's money, by giving each of them of of her own money. In other words, Ann gives as much money to Betty and to carol as each of them already has. Then Betty follows the same set of rules. She gives Ann as much money as Ann has at that time, and gives Carol as much money as Carol has at that time. Finally, Carol executes the same algorithm. She matches Ann's then-current money, and likewise matches Betty's then current noney. FINAL RESULT: Each woman ends up with eight dollars. NOTE: The total is fixed. No money comes into, or leaves, the group during these exchanges. QUESTION: How much money did each women start with?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Let  be the amount Alice has just before the final swap, and let  be the amount that Betty has just before the final swap, Then, since Carol is going to give to Alice and to Betty, and retain 8 dollars for herself, she must, just before the final swap, have  .
So after the final swap, when each will have 8 dollars, Alice has  and Betty has  . Therefore  and 
Now we can make a table of values going backwards:
Alice Betty Carol
After 3rd Swap: 8 8 8
Before 3rd Swap: 4 4 16
(Because Carol must have 8 left after she gives 4 to each of A and B)
Before 2nd Swap 2 14 8
(Because Betty must have 2 to give to A and 8 to give to C)
Before 1st Swap 13 7 4
(Because Alice must have 7 to give to B and 4 to give to C)
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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