The Balancing Shapes

Strategies and Hints

  1. If students assign variables like this:

then one system of equations is

2A + B = 3C + 2D
6B = D + A + C
A + D = 2B + C

It might appear that the problem cannot be solved because there are 4 unknowns and just 3 equations.

  1. Using the variables above, A = , C = 2B, D =.

    For B = 4, A:B:C:D = 13:4:8:3

Solution

Using 3 for the weight of the cone, the left side of the fourth balance equals 12. Since B + C also equals 12, the solution is 2 objects, a sphere and a cube.