Ana gave Billand Clare as much money as each had. Then Bill gave Ana and Clare as much money as each had. Then Clare gave Ana and Bill as much money as each had. Then each of the three people had $24. How much money did each have to bebin with?

Let money with Ana =x , Bill = y, Clare = z

First Ana gives money,

so Ana is left with = x - ( y + z) = x - y - z

Bill now have = 2y

Clare now have = 2z

Now Bill give money similarly,

Bill will have = 2y -(x - y -z + 2z ) = 2y - x + y - z = 3y - x - z

Clare will have = 4z

Ana will have = 2x - 2y -2z

No Clare gives money,

Bill will have: 2(3y - x - z) = 6y - 2x -2z

Clare will have; 4z - ( 3y - x -z + 2x - 2y - 2z ) = 4z - ( y + x - 3z ) = 7z - y - x

Ana will have: 4x - 4y - 4z

Clearly all of them now have,$24

6y - 2x - 2z = 24 => 3y - x - z = 12

7z - y - x = 24

4x - 4y - 4 z = 24 = x - y - z = 6

These equation have infinitely many solutions.

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