Answer:
x +3y = 4x +y
Step-by-step explanation:
A hanger diagram like this is intended to show you that the total weight on the left side is equal to the total weight on the right side.
__
left side
The left side shows 1 triangle and 3 squares. x and y are defined as the weights of the triangle and square, respectively, so the weight on the left side can be represented as ...
x + 3y
right side
The four triangles and 1 square on the right can have their total weight represented as ...
4x +y
balance
The intent of the diagram is to show that the left-side weight is equal to the right-side weight. That equality can be written as ...
x +3y = 4x +y
_____
Additional comment
This problem is not asking for any sort of "solution" or relationship between x and y. We could find such a relationship by solving the equation for y:
x +2y = 4x . . . . subtract y from both sides
2y = 3x . . . . . . . subtract x from both sides
y = (3/2)x . . . . . divide by the coefficient of y
This tells you that the hanger will only be balanced if the weight of a square is half-again as much as the weight of a triangle.
