Answer:
The width of the tank is 5 feet.
Step-by-step explanation:
Let the width of the tank be [tex]w ft[/tex].
Then, the length of the tank will be [tex]l=(w+3)ft[/tex]
and the heigth will be [tex]h=(w-1)ft[/tex].
It was given that the volume of the tank is [tex]160ft^3[/tex].
Recall that the tank is a cuboid or a rectangular prism.
The volume is given by;
[tex]V=l\timesb \times w \times h[/tex].
We substitute the given values into the formula to obtain;
[tex]160=(w+3)(w)(w-1)[/tex]
We expand to obtain
[tex]160=w(w^2-w+3w-3)[/tex]
[tex]160=w(w^2+2w-3)[/tex]
[tex]160=w^3+2w^2-3w[/tex]
[tex]w^3+2w^2-3w-160=0[/tex]
[tex]\Rightarrow w=5[/tex]
Therefore the width of the tank is 5 feet.
