Question

problems 1–2
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 = 6, what is the value of y?

Explanation:

Step1: Analyze left side

Left has 1 triangle ($x$) and 3 squares ($3y$), total weight: $x + 3y$.

Step2: Analyze right side

Right has 4 triangles ($4x$) and 1 square ($y$), total weight: $4x + y$.

Step3: Set equation (balance)

Since hanger is balanced, left = right: $x + 3y = 4x + y$.
Simplify: Subtract $x$ and $y$ from both sides: $2y = 3x$. So equation is $3x = 2y$ (or equivalent).

Step4: Solve for y when x=6

Substitute $x = 6$ into $3x = 2y$: $3(6) = 2y$ → $18 = 2y$.
Divide both sides by 2: $y = \frac{18}{2} = 9$.

Answer:

Equation: $3x = 2y$ (or $x + 3y = 4x + y$), Value of $y$: $9$