To solve this problem, we need to create an equation that describes the balance of weights on each side of the scale. Here's the step-by-step solution:
1. Analyze the Left Side of the Scale:
- On the left side, we have three unit weights and a weight with variable value \( y \).
- So, we can represent the total weight on the left side as:
[tex]\[
1 + 1 + 1 + y = 3 + y
\][/tex]
2. Analyze the Right Side of the Scale:
- On the right side, we have three weights, each with variable value \( y \).
- Therefore, the total weight on the right side is:
[tex]\[
y + y + y = 3y
\][/tex]
3. Equate the Weights on Both Sides:
- Since the scale is balanced, the total weight on the left side must equal the total weight on the right side.
- Hence, we can set up the following equation:
[tex]\[
3 + y = 3y
\][/tex]
So, the equation that describes the relationship between the weights on each side of the scale is:
[tex]\[
3 + y = 3y
\][/tex]
