document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #433453 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "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

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\n" ); document.write( "\n" ); document.write( "So after the final swap, when each will have 8 dollars, Alice has

and Betty has

. Therefore

and

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\n" ); document.write( "\n" ); document.write( "Now we can make a table of values going backwards:
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document.write( "                     Alice        Betty        Carol\r\n" );
document.write( "After 3rd Swap:        8            8            8\r\n" );
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document.write( "Before 3rd Swap:       4            4           16\r\n" );
document.write( "(Because Carol must have 8 left after she gives 4 to each of A and B)\r\n" );
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document.write( "Before 2nd Swap        2           14            8\r\n" );
document.write( "(Because Betty must have 2 to give to A and 8 to give to C)\r\n" );
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document.write( "Before 1st Swap       13            7            4\r\n" );
document.write( "(Because Alice must have 7 to give to B and 4 to give to C)\r\n" );
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document.write( "

\n" ); document.write( "John
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\n" ); document.write( "Egw to Beta kai to Sigma
\n" ); document.write( "My calculator said it, I believe it, that settles it
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$\"The$

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