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?