SOLUTION: 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 scal

Question 264616: 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.
Found 2 solutions by final, jrfrunner:
Answer by final(2) (Show Source): You can put this solution on YOUR website!

Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
Let T=weight of the tetrahedron
Let C=weight of the cube
Let S=weight of the sphere
--
given
scale 1: T+C+S=23
scale 2: 2C+2S=22 ---> C+S=11 divide both sides by 2
scale 3: 2T+S=26
--
substitute C+S=11 from scale 2 into expression from scale 1
T+(C+S)=T+11=23
T=23-11=12
--
substitute T=12 into expression from scale 3
2T+S=2*12+S=26
S=26-24=2
--
substitute T=12, S=2 into expression in scale 1
T+C+S=12+C+2=23
C=23-14=9
==
answer T=12, S=2, C=9
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