Finding Unknown Values

You already know how to find unknown values. Let's prove it.

The scale shows the total weight of the items on it. Here we have five identical squares and the scale reads 40. Since the squares all weigh the same, we can find the weight of a single one by dividing the total weight by the number of squares. 40 / 5= 8. So, one square weighs 8. Let's try another. The scale shows a total weight of 60 made up of two identical triangles and a known weight of 10.

To find the weight of just the triangles, first subtract the known weight from the total. 60 - 10 is 50.

This means the two triangles together weigh 50. Since they're identical, each one weighs half of 50, which is 25.

You found the weights of the unknown shapes by thinking about their relationship to known weights. Let's find the weight of a square. The total weight is 16 made up of two squares and a known weight of 10. If we subtract the 10 from the total, we're left with six.

That's the combined weight of the two squares. So each square must weigh three.

Now that we know the square's weight, we can find the weight of the circle. The second scale has a total weight of 14.

On top, there's one circle, one square, and a known weight of four. We just found that the square weighs 3. So the known items on the scale, the square and the weight add up to 3 + 4, which is 7.

If the total is 14 and the other items weigh 7, the circle must make up the difference. 14 - 7 is 7. The circle weighs 7.

When there are multiple unknowns, first find one value, in this case the square, then use it to find the other. Later, you'll use equations to solve these kinds of problems even faster.