Question

in this balanced hanger diagram, x represents the weight of the triangle and y represents the weight of the square. write an equation using x and y to represent the hanger diagram. if x = 0, what is the value of y?

Explanation:

Step1: Analyze the hanger diagram

Since the hanger is balanced, the weight on the left - hand side is equal to the weight on the right - hand side.
The left - hand side has \(1\) triangle (\(x\)) and \(3\) squares (\(3y\)), so its weight is \(x + 3y\).
The right - hand side has \(3\) triangles (\(3x\)) and \(1\) square (\(y\)), so its weight is \(3x + y\).
Set up the equation: \(x+3y=3x + y\).

Step2: Simplify the equation

Subtract \(x\) from both sides: \(x+3y−x=3x + y−x\), which gives \(3y = 2x + y\).
Subtract \(y\) from both sides: \(3y−y=2x + y−y\), so \(2y = 2x\), and then \(y=x\).

Step3: Find the value of \(y\) when \(x = 0\)

Substitute \(x = 0\) into the equation \(y=x\).

Answer:

The equation is \(x + 3y=3x + y\). When \(x = 0\), \(y = 0\).