# How much did Sanaya and John have at the beginning of their exchange?

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Sanaya gave John as many dollars as John started out with. John then gave Sanaya back as much as Sanaya had left. Sanaya then gave John as back as many dollars as John had left, which left Sanaya broke and gave John a total of \$80.00.
How much did Sanaya and John have at the beginning of their exchange?

posted Sep 4, 2015

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Sanaya starts with X, John starts with Y
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Sanaya gives John what John has. After this Sanaya has X-Y and John has 2Y.
John then gives Sanaya what Sanaya has. After this Sanaya has X-Y + X-Y = 2X - 2Y and John has 2Y - (X-Y) = 3Y - X
Sanaya then gives John as much as John has. After this Sanaya has 2X-2Y - (3Y-X) = 3X - 5Y and John has 3Y-X + 3Y-X = 6Y - 2X
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Sanaya ends up broke => 3X - 5Y = 0
John ends up with 80 => 6Y - 2X = 80
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This gives: Y = 3/5*X and 80 = 18/5*X - 2X = 2/5*X
X = 50 and Y = 30

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