Elementary Lessons in Algebra.
To some people the idea of adding a b c to x y z, or multiplying; letters together, seems the height of absurdity, and they fail to grasp the simplicity of algebra.
In the above puzzle we find a capital illustration of the principle of substitution and the adding of like quantities to both sides of an equation without affecting the equilibrium, so to speak, and an explanation of the reason for so doing to obtain other values. It shows the truth of the algebra axiom that "things which are equal to the same things are equal to each other."
In the first instance we see that a top and three cubes weigh equal to twelve marbles. In the second equation a top alone equals a cube and eight marbles. Now let us add three cubes to each side of the second scales, and as the addition of equal quantities to both sides of an equation does not change their relative values, we have the same equilibrium. By the addition of three cubes to the second pair of scales we have produced the identical values as shown by the first scales. In the first case a top and three cubes = twelve marbles; in the second illustration we have proved that a top and three cubes = four cubes and eight marbles; therefore if four cubes and eight marbles weigh the same as twelve marbles, four cubes = four marbles, so a marble weighs just as much as a cube. It proves therefore that one cube and eight marbles, or nine marbles weighs equal to the top!
20
