Balancing the Scale
If the scale is level, the total weight (or value) on the left equals the total weight on the right.
In the picture:
- Left pan: 4 identical green cubes (each has the same unknown value).
- Right pan: two blocks labeled 12 and 12, so the total is 24.
Let one green cube be x. Because the scale is balanced, we can write the equation:
$$4x = 12 + 12 = 24$$
Now solve for x by dividing both sides by 4:
$$x = 24 ÷ 4 = 6$$
Answer: Each green cube has the value 6.
Remove equal weights
When a scale is balanced, you can remove the same items from both pans without breaking the balance.
Take away three green cubes and the block 4 from both sides. Because we removed the same weights from each pan, the scale stays balanced.
Let the green cube be x.
After removing:
- Left pan: 1 green cube remains
- Right pan: only the block 9 remains
$$x = 9$$
Answer: Each green cube has the value 9.
