Question

1. this hanger is in balance. there are two labeled weights of 4 grams and 12 grams. the three circles each have the same weight. what is the weight of each circle, in grams? \\(\circ\\ \frac{2}{3}\\ \text{g}\\) \\(\circ\\ 1\\ \text{g}\\) \\(\circ\\ \frac{8}{3}\\ \text{g}\\) \\(\circ\\ 8\\ \text{g}\\)

Explanation:

Step1: Set up balance equation

Let $x$ = weight of one circle. The left side total weight equals the right side total weight:
$$3x + 4 = 12$$

Step2: Isolate the variable term

Subtract 4 from both sides:
$$3x = 12 - 4$$
$$3x = 8$$

Step3: Solve for x

Divide both sides by 3:
$$x = \frac{8}{3}$$

Answer:

$\frac{8}{3}$ grams (Option: $\boldsymbol{\frac{8}{3}}$)