Question

A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation x3+6x2-27x=140 can be used to find x.

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

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

Explanation:

Answer 2

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

Explanation:

The equation that desribes the volume of a party-favor bag is

`x^3+6x^2-27x-140=0.`

The solutions of theis equation can be found among divisors of -140. The divisors are:

`\pm1, \pm2, \pm4, \pm5, \pm 7,\pm 10, \pm 14, \pm 20, \pm 35, \pm 70, \pm 140.`

Note that

`5^3+6\cdot 5^2-27\cdot 5-140=125+150-135-140=275-275=0,`

so

`x=5`

is the solution of the equation.

Hence,

the length is 5 inches, the width is 5-3=2 inches and the height is 5+9=14 inches.