Answer & Step-by-step explanation:
Add 1 to both sides.
Multiply both sides by 4.
Take the square root of both sides.
Subtract 5 from both sides.
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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.
According to the problem, the height is 3 inches less than the width therefore we can replace h with the term
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
ANSWER: The width of the box is 10 inches; its length is 22 inches, and its height is 7 inches.