To solve for the width in the formula for the volume of a box, \( V = lwh \), we rearrange the equation to isolate \( w \):
\[ w = \frac{V}{lh} \]
When justifying the rearrangement in terms of units, we need to look at the units of volume and the units of length.
The volume \( V \) has units of cubic inches (\( in.^3 \)), while both length \( l \) and height \( h \) have units of inches (\( in. \)). Therefore, when you divide \( in.^3 \) by \( in. \times in. \) (which is \( in.^2 \)), the units can be simplified as follows:
\[ \frac{in.^3}{in.^2} = in. \]
From this, the correct equation that represents the remaining units is:
Start Fraction in. cubed over in. squared End Fraction equals in.
This shows that when you divide cubic inches by square inches, you are left with inches, which is the correct unit for width.