SOLUTION: 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 ot

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Question 703267: 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 money. 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 josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = Ann's amount at the start
Let = Betty's amount at the start
Let = Carol's amount at the start
They ended up with $8 each, and ,
so, at the start,

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Ann gives Betty dollars and gives Carol dollars
Ann is left with
Betty has
Carol has
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Betty does the same thing as Ann did
She gives Ann , so Ann now has
She gives Carol , so now Carol has
Betty is left with or

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Now Carol does the same thing
She gives Ann and Ann now has
She gives Betty and Betty now has
Carol is left with , or

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Each woman ends up with $8, so
Ann:
(1)
Betty:
(2)
Carol:
(3)
----------------------
(1)
Add (1) and (3)
(1)
(3)

---------------------
(2)
(2)
I know that , so add this to (2)
(2)

and

and
(1)
(1)
(1)
------------------
Ann started with $13
Betty started with $7
Carol started with $4
------------------
check:

OK
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Ann doubled Betty's and Carol's money:
Ann has = $2
Betty has $14
Carol has $8
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Betty doubles carol and Ann's money
Ann has $4
Betty has = $4
Carol has $16
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Carol doubles Ann's and Betty's money
Ann has $8
Betty has $8
Carol has = $8
OK