To solve for the width \( w \) in the volume formula \( V = lwh \), you can rearrange the equation as follows:
- Start with the original formula: \( V = lwh \)
- Rearranging for \( w \), you get: \( w = \frac{V}{lh} \)
Now, let's examine the units involved:
- Volume \( V \) is measured in cubic inches (in³).
- Length \( l \) and height \( h \) are both measured in inches (in).
When you substitute the units into the rearranged equation for width, you have:
\[ w = \frac{V}{lh} \Rightarrow w = \frac{\text{in}^3}{\text{in} \times \text{in}} = \frac{\text{in}^3}{\text{in}^2} \]
This gives us the units for width, which turn out to be in inches (in):
\[ w = \text{in} \]
Therefore, the equation that best represents the unit justification for the rearrangement to solve for the width is:
B. \( \text{in}^3/\text{in}^2 = \text{in} \)
This shows that dividing cubic inches by square inches yields inches, which is consistent with the units for width.