Question

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

Answer 1

Option B

Explanation:

Edge 2021

Answer 2

The dimensions of the the party favor bag are;

Height = 14 inches

Width = 2 inches

Length = 5 inches

Explanation:

The given parameters are;

x³ + 6·x² - 27·x = 140

The dimensions of the party-favor bag are;

Height = (x + 9) inches

Width = (x - 3) inches

Length = x inches

The given equation can be rewritten as follows;

x³ + 6·x² - 27·x - 140 = 0

Using an online application, we have;

x³ + 6·x² - 27·x - 140 = 0 = (x + 4)·(x - 5)·(x + 7)

Therefore, x = -4, 5, or -7

Which gives x = 5, as the length of the party favor bag, x inches, cannot be negative;

Therefore, the dimensions of the the party favor bag are;

Height = (x + 9) inches = (5 + 9) inches = 14 inches

Width = (x - 3) inches = (5 - 3) inches = 2 inches

Length = x inches = 5 inches.