Question

There is a balanced scale. On one side of the scale there are 5 spheres and 1 cube. On the other side of the scale there is 2 spheres and 3 cubes. The question is:
If cubes weigh 150 grams each, how much do the spheres weigh?

Answer 1

The scale has two sides:
The Left Hand Side (LHS) and the Right Hand Side (RHS).
Let the weight of the sphere be represented as s
Let the weight of the cube be represented as c

Let the LHS have the 5 spheres and 1 cube, represented as = (5s + 1c)
Let the RHS have the 2 spheres and 3 cubes, represented as = (2s + 3c)

If the cube c, weighs 150 gram,  c = 150g

Since the scale is balanced, therefore the weights on the LHS would be equal to the weights on the RHS.

Therefore:        (5s + 1c) = (2s + 3c),        c = 150.
                         (5s + 1*150) = (2s + 3*150)
                         (5s + 150) = (2s + 450)    collect like terms.
                          5s  -  2s    =  450 - 150
                                    3s    =    300        Divide both sides by 3
                                       s    =   300/3
                                        s    =  100
Therefore the sphere  weighs  100 gram each.