Physical Equations

In this example, we are given this image of a balance scale where the left side is perfectly balanced with the right side.

The circles are symbols that represent cups and that the squares represent gram cubes.

That means that two cups and three gram cubes are balanced with one cup and seven gram cubes.

In order for the scale to be perfectly balanced, what is the value of each cup? Or if we're thinking about this as a scale, what is the weight of each cup?

All of the cups in a single problem will have the same weight. So how can we figure this out?

To start, let's actually set up this problem using a problem solving mat with cups and gram cubes. Two cups and three gram cubes on the left side, one cup, and seven gram cubes on the right side.

We can use trial and error to find the value of each cup. To do that, let's start by placing one gram cube in each cup.

If each cup weighs one gram, the left side equals five and the right side is equal to eight. Both sides are not equal when the value of the cup is one.

So let's repeat this process by adding another cube to each cup. Now the left side is equal to seven and the right side is nine. The sides are not in balance when the value of each cup is two.

So, let's add a third cube to each cup. Now, the left side is equal to nine, and the right side is equal to ten. We're getting closer, but we're not perfectly balanced yet.

Let's try one more cube. When each cup contains four cubes, the left side is equal to eleven, and the right side is also eleven.

We have an answer. The value of each cup is four.

We can check that mathematically using numbers. Four plus four plus three equals four plus seven. Eleven equals eleven. It checks out.

And now, you're ready to begin solving for unknown values of cups using trial and error.