Question

The height of a box that joan is shipping is 3 inches less than the width of the box. the length is 2 inches more than twice the width. the volume of the box is 1540 in3. what are the dimensions of the box?

Answer 1

We first recall the formula for the volume of a rectangular box:
$V=l*w*h$ where l is its length, w is the width, and h is the height.

According to the problem, the height is 3 inches less than the width therefore we can replace h with the term $w-3$. Additionally, the length of the box is 2 inches more than twice the width therefore the length can also be replaced with $2w+2$.

We can notice that the equation will just have one unknown variable because we already know the volume of the box. We can then solve for this variable (w):

$1540=(2w+2)w(w-3)$
$1540=(2w+2)(w^{2}-3w)$
$1540=2w^{3}-6w^{2}+2w^{2}-6w$
$0=2w^{3}-4w^{2}-6w-1540$

Solving the cubic equation we'll get $w=10$ and two complex number solutions. We'll just need to solve for the length and height using the value of the width:

$l=2w+2=2(10)+2=22$
$h=w-3=10-3=7$

ANSWER: The width of the box is 10 inches; its length is 22 inches, and its height is 7 inches.