Question

here is a balanced hanger. what is the weight of one square if a triangle weighs 4 grams?

Explanation:

Step1: Set up equation based on balance

Let the weight of one square be \(x\) grams.
The left - hand side of the hanger has \(1\) triangle and \(2\) squares, so its weight is \(4 + 2x\) grams.
The right - hand side of the hanger has \(3\) triangles and \(1\) square, so its weight is \(3\times4+x\) grams.
Since the hanger is balanced, we have the equation \(4 + 2x=3\times4+x\).

Step2: Simplify the equation

Simplify \(3\times4 = 12\), so the equation becomes \(4 + 2x=12+x\).
Subtract \(x\) from both sides: \(4 + 2x-x=12+x - x\), which gives \(4+x=12\).

Step3: Solve for \(x\)

Subtract \(4\) from both sides: \(x=12 - 4\).

Answer:

\(8\) grams