Given that a jewelry
box has a length that is 2 inches longer than the width and a height
that is 1 inch smaller than the width.
Let the width of the box be w, then the length of the box is given by l = w + 2 and the height of the box is given by h = w - 1.
The volume of a box is given by
[tex]V=l\times w\times h \\ \\ =w(w+2)(w-1) \\ \\ =w(w^2+w-2)=w^3+w^2-2w[/tex]
Given that the volume of the box is 140
cubic inches. Thus
[tex]w^3+w^2-2w=140[/tex]
Thus, the width of the jewelry box is obtained as follows
[tex]w^3+w^2-2w=140 \\ \\ \Rightarrow w^3+w^2-2w-140=0 \\ \\ \Rightarrow(w-5)(w^2+6w+28)=0 \\ \\ \Rightarrow w=5[/tex]
Therefore, the width of the jewelry box is 5 inches.
*Note that [tex]w^2+6w+28=0[/tex] gives complex roots, so we did not use it.
