Answer:
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
