A box shaped like a rectangular prism has a height of 17 in. and a volume of 2,720 in.^3. The length is 4 inches greater than twice the width. What is the width of the box?
a. -10 in.
b. 8 in.
c. 20 in.
d. 40 in.
Let the width of the box be x inches.
Given that the length is 4 inches greater than twice the width, the length = 2x + 4 inches.
The volume of a rectangular prism is given by the formula V = length x width x height.
Given that the height = 17 in. and the volume = 2,720 in^3, we can write the equation as:
2,720 = (2x + 4) x x x 17
2,720 = (2x^2 + 4x) x 17
2,720 = 34x^2 + 68x
2,720 = 34x^2 + 68x
0 = 34x^2 + 68x - 2,720
0 = x^2 + 2x - 80
0 = (x - 8)(x + 10)
So, the possible solutions for x are x = 8 and x = -10
Since the width cannot be negative, the width of the box is 8 inches.
Therefore, the answer is option b. 8 in.