Question

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. What is the width of the tank?

Answer 1

Answer:

The width of the tank is 5 feet.

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 $x.$

So, length is $x+3.$

And, height is $x-1.$

The volume of tank = 160 cubic feet.

Now, to get the width we put formula:

Volume = length × width × height.

$160=(x+3)\times x\times (x-1)$

$160 =x(x^2-x+3x-3)$

$160=x(x^2+2x-3)$

$160=x^3+2x^2-3x$

Subtracting both sides by 160 we get:

$0=x^3+2x^2-3x-160$

$x^3+2x^2-3x-160=0$

Now, on solving the equation we get:

$x=5.$

The width = 5 feet.

Therefore, the width of the tank is 5 feet.