A box shaped like a rectangle prism has a height of 17 inches and a volume of 2,720 in^2. The length is 4 inches greater than twice the width. What is the width of the box?
width --- x
length --- 2x+4
(17)(x)(2x+4) = 2720
x(2x+4) = 160
2x^2 + 4x - 160=0
x^2 + 2x - 80 = 0
(x+10)(x-8) = 0
x = -10 , which would make no sense
or
x = 8
The box is 8 inches wide
check:
w=8
l= 20
h=17
V = 8x20x17=2720
All looks good
Yes, this is the correct answer, good job!
To find the width of the box, we need to set up an equation based on the given information.
Let's assume the width of the box is "w" inches.
According to the problem, the length is "4 inches greater than twice the width." So the length would be 2w + 4 inches.
Now, we can calculate the volume of the box using the formula:
Volume = Length × Width × Height
Given that the volume is 2,720 in^2 and the height is 17 inches, we can substitute the values into the formula and solve for the width:
2,720 = (2w + 4) × w × 17
Now, simplify the equation:
2,720 = 34w² + 68w
Rearrange the equation to get it in the form of a quadratic equation:
34w² + 68w - 2,720 = 0
Now, we need to solve this quadratic equation for "w." We can either factor it or use the quadratic formula.
Let's use the quadratic formula:
w = (-b ± √(b² - 4ac)) / (2a)
In our equation, a = 34, b = 68, and c = -2,720.
Substituting these values into the quadratic formula, we get:
w = (-68 ± √(68² - 4*34*(-2,720))) / (2*34)
Now, we can calculate the width using a calculator:
w ≈ (-68 ± √(4,624 + 369,920)) / 68
w ≈ (-68 ± √(374,544)) / 68
w ≈ (-68 ± 612) / 68
Now, we have two possibilities for the width:
1. w ≈ (-68 + 612) / 68
w ≈ 544 / 68
w ≈ 8 inches
2. w ≈ (-68 - 612) / 68
w ≈ -680 / 68
w ≈ -10 inches
Since the width of a box cannot be negative, we can discard the second possibility.
Therefore, the width of the box is approximately 8 inches.