Answer:
The width of the tank is <u>5 feet</u>.
Step-by-step explanation:
Given:
A tank's length is 3 feet longer than its width.
The height is 1 foot less than the width.
The volume of the tank is 160 cubic feet.
Now, to find the width of the tank.
Let the width of the tank be ![x.](https://tex.z-dn.net/?f=x.)
So, length is ![x+3.](https://tex.z-dn.net/?f=x%2B3.)
And, height is ![x-1.](https://tex.z-dn.net/?f=x-1.)
The volume of tank = 160 cubic feet.
Now, to get the width we put formula:
Volume = length × width × height.
![160=(x+3)\times x\times (x-1)](https://tex.z-dn.net/?f=160%3D%28x%2B3%29%5Ctimes%20x%5Ctimes%20%28x-1%29)
![160 =x(x^2-x+3x-3)](https://tex.z-dn.net/?f=160%20%3Dx%28x%5E2-x%2B3x-3%29)
![160=x(x^2+2x-3)](https://tex.z-dn.net/?f=160%3Dx%28x%5E2%2B2x-3%29)
![160=x^3+2x^2-3x](https://tex.z-dn.net/?f=160%3Dx%5E3%2B2x%5E2-3x)
<em>Subtracting both sides by 160 we get</em>:
![0=x^3+2x^2-3x-160](https://tex.z-dn.net/?f=0%3Dx%5E3%2B2x%5E2-3x-160)
![x^3+2x^2-3x-160=0](https://tex.z-dn.net/?f=x%5E3%2B2x%5E2-3x-160%3D0)
Now, on solving the equation we get:
![x=5.](https://tex.z-dn.net/?f=x%3D5.)
The width = 5 feet.
Therefore, the width of the tank is 5 feet.