Bags and Marbles

In order to learn how to solve equations, we are going to use bags and marbles as a model for how to think about the equations.

Bags will represent the variable that we are solving for.
Marbles will represent the constants.

The goal for solving an equation is to find the value of the variable. An easy strategy for finding the number of marbles in each bag is to get the variables (bags) on one side and the marbles (constants) on the other side.

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Example 1

How many marbles are in each bag?

For this balance, each bag contains the same number of marbles. For this model, let's assume that the bags in our models weigh almost nothing compared to the marbles.

The balance is perfectly level, which means that one bag and seven marbles weigh the same amount as two bags and three marbles.

If we remove one bag of marbles from each side, the balance will still be level. There will be seven marbles on the left side and one bag and three marbles on the right.