Question

The pans shown are balanced. Use the SubtractionProperty of Equality to find which shapes are equalto one purple pyramid.

Answer 1

According to the Subtraction property of equality, the equality of an expression holds true if the same finite number is subtracted from both sides of the equality,

$a=b\Rightarrow a-c=b-c$

Now, observe the given figure carefully.

We will use the above-mentioned property to get rid of the common shapes that exist on both sides. Here, the balance represents equality between both sides.

Consider that the pans are initially balanced. And both sides contain a red cube. So we can subtract or eliminate the red cube and the equality will still hold true.

Similarly, we can eliminate the blue sphere.

At this point, we have the purple pyramid and a yellow diamond on the left side, and on the right side, we have 4 pieces of yellow diamond.

Observe that one piece of yellow diamond is common to both sides, so it can also be eliminated from both sides.

After this, the left side will contain only the purple pyramid while the right side contains 3 yellow diamonds. Since we are always using the subtraction property to eliminate the shapes, the balance must be maintained throughout the process.

At last, there must exist a balance between the left side containing the purple pyramid only, and the right side containing 3 yellow diamonds.

Therefore, it can be concluded that one purple pyramid is equal to 3 yellow diamonds.