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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 It's elementary (elementary math) | Comment 9 of 12 |

(W-A) = (D-A). (An expression times itself equals the expression squared)

(W-A) = (D-A) (Square root)

That's where you went wrong.

Two numbers that are of opposite sign but equal absolute value will also have equal squared value.

 

 

Edited on November 3, 2007, 6:46 am
  Posted by Penny on 2005-02-22 21:17:31

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