2 Variable Scenario Concept (Level 1)

The strategy involves organizing the two scenarios into a table to systematically compare them. By making one of the variables (items) equal in both scenarios, students can eliminate that variable and find the value of the remaining item through subtraction. The Problem Example Scenario 1: 2 identical earrings and 3 similar necklaces cost $95. Scenario 2: 3 such earrings and 2 such necklaces cost $105. Goal: Determine the cost of one earring. Key Instructional Steps Draw the Table: Create a table with columns for Earrings (E), Necklaces (N), and the total Cost. Identify the Target Item: Note which item the question is asking for (Earrings). Eliminate the Unwanted Item: To find the cost of earrings, you must make the number of necklaces equal in both scenarios. Find a common multiple for 3 and 2 (which is 6). Multiply all values in Scenario 1 by 2. Multiply all values in Scenario 2 by 3. Find the Difference: Subtract the totals of the adjusted rows (Row 2 minus Row 1) to isolate the cost of the remaining earrings. Why This Method Works This approach is a visual, non-algebraic way to perform simultaneous equations. By equalizing the "unwanted" item, any difference in the final cost is directly attributed to the difference in the number of the "target" item. This allows students to solve for a single unit value simply and accurately.