Let's find the value of unknown quantities by building and solving equations. This balance scale will help us visualize the process. First, let's write an expression for the left side of the scale. It has two squares of unknown weight S, which is 2 S plus a weight of 12. The left side is 2 S + 12. A balanced scale means both sides are equal. The left is 2 S + 12. The right side has 4 S squares, so its weight is 4 S. The equation is 2 s + 12 = 4 s.
To solve for s, we need all s squares on one side. To keep the scale balanced, we must remove the same amount from both sides. We can remove 2s from both sides.
Removing 2 s from each side leaves us with 12 on the left and 2 s on the right. So 12 = 2 s. If 2 s squares weigh 12, then 1 s must be 6.
We started with 2 S + 12 = 4S. By making balanced changes, we found the solution is S= 6. Let's look at a different problem. The left has five circles of weight C, so that's 5 C. The right has three C circles and a weight of 14. The full equation is 5 C= 3 C + 14.
Now, let's find the solution. We can remove 3 C from both sides to keep the scale balanced. This leaves 2 C on the left and 14 on the right. The equation becomes 2 C= 14. If 2 C is 14, then each C must be 7.
You've seen how to translate a visual problem into an equation and then solve it systematically.