Question

A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation x^3+6x^2-27x=140 can be used to find x.
height(x+9)in width(x-3)in length x in
What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer.

The length is 7 inches, the width is 4 inches, and the height is 16 inches.
The length is 5 inches, the width is 2 inches, and the height is 14 inches.
The length is 4 inches, the width is 1 inch, and the height is 13 inches.
The length is 3 inches, the width is 0 inches, and the height is 12 inches.

Answer 1

For this case we have the following equation for the volume:

$x ^ 3 + 6x ^ 2-27x = 140$

Rewriting the equation we have:

$x ^ 3 + 6x ^ 2-27x-140 = 0$

We factor the equation to find the roots of the polynomial.

We have then:

$(x-5) (x + 4) (x + 7) = 0$

Then, we discard the negative roots, because the dimensions of the figure must be positive.

We have then that the length is:

$x = 5$

The height is:

$x + 9 = 5 + 9 = 14$

The width is:

$x-3 = 5-3 = 2$

Thus, the dimensions are:

$5 * 14 * 2$

Answer:

The length is 5 inches, the width is 2 inches, and the height is 14 inches.

Answer 2

The answer is:
B. The length is 5 inches, the width is 2 inches, and the height is 14 inches.
Hope this helps! :)