Question

Write an equation using x and y to represent the hanger.

Answer 1

Answer:

Step-by-step explanation:

Givens

The triangle is x

The square is y

Left side

x + 3y is the weight

Right side

4x + y is the weight.

The weights are equal because the hanger is balanced.

Balance equation

x + 3y = 4x + y                 Subtract x from both sides

x-x + 3y = 4x-x + y           Combine

3y = 3x + y                       Subtract y from both sides

3y - y = 3x + y - y             Combine

2y = 3x

Answer

2y = 3x

Answer 2

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.