Cubic container

[phillygurl]

A cubic container, with sides of length, x inches, has a volume equal to x3 cubic inches. The height of the container was decreased and the length was increased so that the volume is now modeled by the expression

x^3 + 4x^2 - 5x

By how many feet were the height and length changed?
The Hint that was provided was: Volume = length times width times height

I'm stuck on this because I don't know what x is?

So what I was doing was:
x(x^2 + 4x - 5)
= x( x - 1)(x + 5)

does that mean that x = -1
and x = 5

when I check
5(5x5 + 4(5) - 5)
= 5 (25 + 20 - 5)
= 5(25 + 15)
= 5(40)
= 200

-1(-1x-1 + 4(-1) -5)
= -1 (1 + (-4) - 5)
= -1(1 + (-9))
= -1(-8)
= 8

I don't get it?????

 

[wjm11]

A cubic container, with sides of length, x inches, has a volume equal to x3 cubic inches. The height of the container was decreased and the length was increased so that the volume is now modeled by the expression

x^3 + 4x^2 - 5x

By how many feet were the height and length changed?
The Hint that was provided was: Volume = length times width times height

I'm stuck on this because I don't know what x is?

So what I was doing was:
x(x^2 + 4x - 5)
= x( x - 1)(x + 5)

does that mean that x = -1
and x = 5

Your math (the factoring) was good. You just need a little help with interpretation. Notice that you’ve factored the volume into three terms:

V = x( x - 1)(x + 5)

Notice also that in the problem statement, the height and length changed but not the width. Your three factors represent the three dimensions of the cube. The x is the width. The (x – 1) expression represents the dimension that decreased – the height decreased by 1 inch. The dimension that increased (x + 5) is the length, which increased by 5 inches. Make sense now?

Also notice that we are working in inches, but the problem asks, “By how many feet were the height and length changed?” Be sure to convert inches to feet for your final answer.

Hope that helps.

 

[phillygurl]

I follow you but still haven't slam dunked as of yet.

The x is the width. The (x – 1) expression represents the dimension that decreased – the height decreased by 1 inch. The dimension that increased (x + 5) is the length, which increased by 5 inches.

X(?) = 4(5)^2 - 5(-1)
x = 4(5 x 5) - (-5)
x = 4(25) - (-5)
x = 100 + 5
x = 105

so then
105w = 100l + 5h

V = L x W x H
105 x 100 x 5 = 52500 inches

but they want the L & H converted to feet

so my height would be less than 1/2 a foot
and my length 8ft approx.

 

[wjm11]

This problem does not have have exact dimensions for either the cube or the right rectangular box. We can only state what the *changes* are to the dimensions -- not what the actual dimensions are. The answer is that the height decreased by one inch and the length increased by five inches. Do not try to plug in values for x. X could be almost anything.

 

[phillygurl]

oh...ok