Arectangular box has dimensions 5ft by 4ft by 3ft. increasing each dimension of the box by the same amount yields a new box with volume seven times the old. use the aleks graphing calculator to find how much each dimension of the original box was increased to create the new box. round your answer to two decimal places.

Each dimension increased by 3.53 ft

Step-by-step explanation:

* Lets explain how to solve the problem

- A rectangular box has dimensions 5 ft by 4 ft by 3 ft

∵ The volume of the rectangular box = l × w × h , where

   l , w , h are its dimensions

∵ l = 5 ft , w = 4 ft , h = 3 ft

∴ Its volume = 5 × 4 × 3 = 60 ft³

- Each dimension of the box is increasing by the same amount

 to yield a new box

- Let each dimension will increase by x ft

∴ The new dimensions are l = (5 + x) , w = (4 + x) , h = (3 + x)

- The volume of the new box is seven times the old

∵ The volume of the old box is 60 ft³

∴ The volume of the new box = 7 × 60 = 420 ft³

∵ The volume of new box = (5 + x)(4 + x)(3 + x)

∴ (5 + x)(4 + x)(3 + x) = 420

- Multiply the 3 brackets

∵ (5 + x)(4 + x) = 20 + 9x + x²

∴ (20 + 9x + x²)(3 + x) = 60 + 47x + 12x² + x³

∴ 60 + 47x + 12x² + x³ = 420

- Subtract 420 from both sides and arrange the terms

∴ x³ + 12x² + 47x - 360 = 0

- Use the ALEKS graphing calculator to find x

∴ x = 3.53

* Each dimension increased by 3.53 ft

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