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 Proving a witch weighs the same as a duck (Posted on 2005-02-21)
Suppose the witch weighs W pounds, and the duck weighs D pounds. Also, suppose their average weight is A pounds. (Their combined weight is 2A)

W + D = 2A. (Given)
W = 2A - D. (Subtract D)
W - 2A = -D (Subtract 2A)
W(W - 2A) = W(-D) (Multiply by W)
W(W - 2A) = (2A - D)(-D) (Substitute 2A-D for W using the given equation)
W² - 2AW = -2AD + D² (Distribute)
W² - 2AW + A² = D² - 2AD + A² (Add A²)
(W-A)(W-A)=(D-A)(D-A). (Factor)
(W-A)² = (D-A)². (An expression times itself equals the expression squared)
(W-A) = (D-A) (Square root)

In other words, a witch weighs the same as a duck.

Where did I go wrong?

 Submitted by Dustin Rating: 3.0000 (4 votes) Solution: (Hide) From (W-A)^2 = (D-A)^2 to (W-A) = (D-A). Assuming the witch weighs more than the duck, the average weight(A) is greater than the duck's weight(D) and less than the witch's(W). So W-A is positive, while D-A is negative. It's like trying to prove 3=-3 because they are both the square root of 9. I could take the square root, but it would end up (W-A) = (-D+A). Adding A to both sides gives 1).

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