Question

A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation 23 + 6,2 - 27x= 140 can be used to find x. Height: (x+9) in. Width: (2 - 3) in Length: xin. What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer. O The length is 7 inches, the width is 4 inches, and the height is 16 inches. O The length is 5 inches, the width is 2 inches, and the height is 14 inches. O The length is 4 inches, the width is 1 inch, and the height is 13 inches. O The length is 3 inches, the width is O 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 < br/ >`

Rewriting the equation we have:

`x^3+6x^2-27x=140=0 < br/ >`

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

We have then:

`(x-5)(x+4)(x+7)=0 < br/ >`

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

We have then that the length is:

`x=5 < br/ >`

The height is:

`x+9=5+9=14 < br/ >`

The width is:

`x-3=5-3=2 < br/ >`

Thus, the dimensions are:

`5*14*2 < br/ >`

Answer:

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