The Mystery Box

Pre-Algebra · Axiom Academy

A sealed box of unknown weight sits on a balance scale. You can't peek inside — but you can still figure out exactly what it weighs. The whole idea of solving, in one move Algebra can feel like it's full of mysterious letters. But a letter like x is just a stand-in for a number you don't know yet — a sealed box on a balance scale. And there's one simple move that cracks every box open. The scale below is perfectly level, so the two sides weigh the same: a mystery box and three 1‑pound weights balance eight 1‑pound weights. Watch what happens when we lift the same three weights off both pans at once. Take the same amount off both sides and the scale stays level — so when the box stands alone, the weights left facing it are its hidden value. Here a mystery box and four weights sit on the left, seven weights on the right. Drag the dial to set how heavy you think the box is. Too light and the left side floats up; too heavy and it sinks. Find the weight that makes the scale sit perfectly level. When both sides read the same, the scale is balanced — and the box's weight is no longer a mystery. This time the box has two weights stacked beside it on the left, against nine on the right. Instead of guessing, do the move from the opening: drag to lift the same number of weights off both pans. Take away just enough that the box is left standing completely alone.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.