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)
W = D (Add A)

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

Where did I go wrong?

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