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)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?