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?

We first recall the formula for the volume of a rectangular box:
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 . Additionally, the length of the box is 2 inches more than twice the width therefore the length can also be replaced with .

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):






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




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