Question

The dimensions of a chocolate box are: height=x + 2 inches, length=2x+5 inches, and width=4x-1 inches. If the volume of the chocolate box is 605 cubic inches, what is the value of x?

Answer 1

I hope this helps you

Answer 2

Answer:

To begin to answer your question you would need to know that the formula for the volume of a rectangular prism is the following: $V=lwh$. Now its just a manner of substitutions.

Step-by-step explanation:

$V=605 \text{in}^3$

Then one can also state the following:

$V=(x+2)(4x-1)(2x+5)$

Following up with this substitution:

$605=(x+2)(4x-1)(2x+5)$

Proceeding with a FOIL procedure:

$605=(4x^2+8x-x-2)(2x+5)$

$605=8x^{3}+34x^{2}+31x-10$

$0=8x^{3}+34x^{2}+31x-615$

Using PRZs:

$PRZs=\frac{\text{Factors of Constant Term}}{\text{Factors of Highest Power}}=\frac{\pm 1,\pm 3, \pm 5, \pm 41, \pm 615}{\pm 1, \pm 2, \pm 4, \pm 8}$

By graphing it one can identify that 3 is a solution so plugging it in and using synthetic division.

$\begin{array}{ccccc}3|& 8 & 34 & 31 & -615\\ \ \ |& & 24 & 174 & 615 \\ & 8 & 58 & 205 &0 \end{array}$

Giving the following the polynomial:

$0=(x-3)(8x^2+58x+205)$

Now one can evaluate the discriminant of that quadratic:

$58^2-4(8)(205)=-3196$

Because it is negative one knows that it produces imaginary solutions. Therefore the only real solution is $x=3$. Therefore the dimension of the box is the following: $5\text{in},11\text{in}, 11\text{in}$