Question

lesson practice
8.4.03
problems 1-2: in this balanced hanger diagram, ( x ) represents the weight of the triangle and ( y ) represents the weight of the square.

1. write an equation using ( x ) and ( y ) to represent the hanger diagram.
2. if ( x = 6 ), what is the value of ( y )? show or explain your thinking.

Explanation:

Problem 1

Step1: Analyze left side

Left has 1 triangle and 3 squares: $x + 3y$

Step2: Analyze right side

Right has 4 triangles and 1 square: $4x + y$

Step3: Set equal (balanced)

Since balanced, $x + 3y = 4x + y$

Step1: Use equation from 1

We have $x + 3y = 4x + y$, and $x = 6$

Step2: Substitute x=6

$6 + 3y = 4(6) + y$

Step3: Simplify right side

$6 + 3y = 24 + y$

Step4: Subtract y and 6

$3y - y = 24 - 6$ → $2y = 18$

Step5: Solve for y

$y = \frac{18}{2} = 9$

Answer:

$x + 3y = 4x + y$

Problem 2