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.