The problem presents a balanced hanger with a weight of 27 on one side and three weights labeled $v$ on the other side. We need to find the value of $v$ that makes the equation true.

1. Problem Description

The problem presents a balanced hanger with a weight of 27 on one side and three weights labeled $v$ on the other side. We need to find the value of $v$ that makes the equation true.

2. Solution Steps

The hanger represents the equation:

$27 = v + v + v$

$27 = 3v$

To find the value of $v$, we need to divide both sides of the equation by 3:

$\frac{27}{3} = \frac{3v}{3}$

$9 = v$

Therefore, $v = 9$.

3. Final Answer

$v = 9$