Question

1. a scale like the one shown is balanced when it has 18 1-pound bricks on one side and 3 equally sized pieces of gold on the other. how much does each piece of gold weigh? answer with supporting work:

Explanation:

Step1: Find total weight of bricks

Each brick is 1 - pound, and there are 18 bricks. So total weight of bricks is \(18\times1 = 18\) pounds.

Step2: Let weight of each gold piece be \(x\)

There are 3 gold pieces, so total weight of gold is \(3x\) pounds. Since the scale is balanced, total weight of bricks equals total weight of gold. So \(3x=18\).

Step3: Solve for \(x\)

Divide both sides of the equation \(3x = 18\) by 3. \(x=\frac{18}{3}=6\).

Answer:

Each piece of gold weighs 6 pounds.