Here is a hanger that is in balance. We don’t know how much any of its shapes weigh. How could you change the number of shapes on it, but keep it in balance? Describe in words or draw a new diagram.

We can take away the two circles from both sides. We don't know the weight of each circle, but we know that the circles on each side balance each other out. Meaning that taking away those circles does not change the balance. Similarly, we can take away two squares from each side to keep things balanced as well.

After those subtractions, we're left with 2 squares on the left side and nothing else. On the right side, we have 4 triangles only.

2 squares balance with 4 triangles, which must mean 1 square balances with 2 triangles (divide both values by 2).

If you add a square to one side, you must add 2 triangles to the other side to keep things balanced.

Going back to the original diagram, we can have the following on the left side

And on the right side we would have

This new configuration is balanced. I added the 2 triangles to the left side while the right side got the square.

There are other configurations possible because we can add as many squares to each side, as long as we add 2 triangles per extra square. Also, the order of the shapes on either side doesn't matter. All that matters is the total weight pulling down.

Also, we could easily add the same shape to both sides as possibly the easiest way to change the configuration. For instance, if you add a circle to both sides, then things stay balanced. So again, there are many ways to answer this.

answer: the correct answer is -32

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