Question

(7 points, A -REL.2.4) A packing company is doing an inventory of boxes. Their most popular box is displayed below. Use the formula for volume of a box, V = lwh. If the volume is 40f * t ^ 3 , find the value of x. Then find the length and width of the box. State any extraneous solutions.

Answer 1

The extraneous solution is x = -5/6

Length = 4 ft

Width = 5 ft

Explanation:

Length = 3x - 5 ft

Width = 2x - 1 ft

Height = 2 ft

Volume = 40 ft^3

Volume = length × width × height

40 = (3x - 5)(2x-1)(2)

40 = (6x^2 - 3x - 10x + 5)(2)

40 = 12x^2 - 6x - 20x + 10

12x^2 - 26x + 10 - 40 = 0

12x^2 - 26x - 30 = 0

Divide through by 2

6x^2 - 13x - 15 = 0

Solve using factorization method

(6x + 5) (x - 3) = 0

6x + 5 = 0

6x = -5

x = -5/6

Or

x - 3 = 0

x = 3

The extraneous solution is x = -5/6

Length = 3x - 5 ft

= 3(3) - 5

= 9 - 5

= 4 ft

Width = 2x - 1 ft

= 2(3) - 1

= 6 - 1

= 5 ft