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Proving a witch weighs the same as a duck (Posted on 2005-02-21) Difficulty: 2 of 5
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)
W - 2AW = -2AD + D (Distribute)
W - 2AW + A = D - 2AD + A (Add A)
(W-A)(W-A)=(D-A)(D-A). (Factor)
(W-A) = (D-A)². (An expression times itself equals the expression squared)
(W-A) = (D-A) (Square root)
W = D (Add A)

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

Where did I go wrong?

See The Solution Submitted by Dustin    
Rating: 3.0000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Who says they don't weight the same? (solution) | Comment 1 of 12

It is true that

(W-A)(W-A) = (D-A)(D-A)

but unless W=D one of the sides is two negatives and the other is two positives.  In the square root step you erroneously converted both to positives.

Those darned square roots.


  Posted by Jer on 2005-02-21 15:05:24
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