Question

Can anyone help me with this question, at least show me how to set up which equations to solve it?

"A shipping company designs a container that is a rectangular prism with a length that is 3 inches more than its width and a height that is 1 inch less than its width. If the volume of the container is 160 cubic inches, find its dimensions. Show all your work."

Answer 1

Did you draw a picture and label it ?

Answer 2

This is basically what I have drawn, I'm just not completely sure how to go about solving it.

Answer 3

the volume is length*width*height or in this case
x(x-1)(x+3) = 160
multiply out. what do you get ?

Answer 4

I really don't want to sound stupid, but I kind of need a refresher on how to do that, like what steps to take to multiply it out and find the dimensions, like solving for x or something.

Answer 5

This gives the basics
http://www.khanacademy.org/math/algebra/polynomials/multiplying_polynomials/v/multiplication-of-polynomials

in this case, first do (x-1)*(x+3)
if we do FOIL (first terms), outer terms, inner terms, last terms
x*x +x*3 + -1*x + -1*3
or x^2 +2x -3

(the other way is "distribute" the (x-1): (x-1)*x + (x-1)*3
now distribute again: x^2 -x + 3x -3 and combine the x terms: x^2 + 2x-3

now multiply by x (because we are doing x*(x-1)*(x+3) )
we get x*(x^2 + 2x-3) = x^3 +2x^2-3x
that is the volume and it equals 160:

x^3 +2x^2-3x= 160
or, subtracting 160 from both sides, to put this cubic equation in standard form:
x^3 + 2x^2 -3x -160 =0

Answer 6

cubics are complicated to solve.
see http://en.wikipedia.org/wiki/Cubic_function
for the hairy details.

I imagine they want you to use a graphing calculator to solve this?

or, use wolfram (which may or may not be cheating, depending on what you are learning...)
http://www.wolframalpha.com/input/?i=x%5E3+%2B+2x%5E2+-3x+-160+%3D0

Answer 7

wolfram found x=5. If we use that in your picture, we find
width=5, height = 4 and length= 8

Answer 8

as a check: 5*4*8= 20*8= 160 cu. inches which matches what they told us is the volume.

Answer 9

Thank you so much! That helped tremendously!