geometry for teachers elementary problem

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At a carnival, players are to guess the weight of three objects; a tetrahedron, sphere, and a cube. Players are given three different combinations of these items on scales. On scale #1, there is a tetrahedron, a cube, and a sphere. The weight displayed on the first scale is 23 kg. On scale #2, there are two cubes, and two spheres. The weight displayed on the second scale is 22kg. On scale #3, there are two tetrahedron, and one sphere. The weight displayed on the third scale is 26 kg. Determine the weights of the items, and explain how you could solve this problem algebraically. Find the solution and general solution!

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