To find the width of the box, we can use the formula for the volume of a rectangular prism, which is Volume = Length × Width × Height. Given that the volume is 2720 in³ and the height is 17 in, we can first express the volume in terms of width.
Let’s denote the width of the box as w. According to the problem, the length is 4 inches greater than twice the width, which we can write as l = 2w + 4.
Substituting the expressions for length and height into the volume formula gives us:
2720 = (2w + 4) × w × 17
Now we can simplify this equation:
2720 = 17(2w² + 4w)
2720 = 34w² + 68w
Next, we rearrange this equation to bring all terms to one side:
34w² + 68w – 2720 = 0
To make calculations easier, we can divide the entire equation by 34:
w² + 2w – 80 = 0
Now, we can factor the quadratic equation or use the quadratic formula. It factors neatly:
(w + 10)(w – 8) = 0
This gives us two potential solutions for w: w + 10 = 0 or w – 8 = 0. Solving these, we get:
w = -10 (not a valid solution since width can’t be negative) and w = 8.
Thus, the width of the box is 8 inches.