## 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.  Now three marbles can be removed from each side. This leaves four marbles on the left and one bag on the right. This means there are four marbles in each bag. Check to make sure the answer is correct. Example 2 Two marble bags plus 12 marbles weighs the same amount as four marble bags plus two marbles. How many marbles are in each bag? [show answer] Example 3 Four marble bags plus 1 marble weighs the same amount as 1 marble bag plus 13 marbles. How many marbles are in each bag? [show answer] # Self-Check

Question 1 Three marble bags plus 6 marbles weighs the same amount as 4 marble bags plus 1 marble. How many marbles are in each bag?

Question 2 Two marble bags plus 7 marbles weighs the same amount as 1 marble bag plus 10 marbles. How many marbles are in each bag? 