SOLUTION: A storage company needs to design a new storage box that has twice the volume of its largest box. Its largest box is 5 ft long, 4 ft wide, and 3 ft high. The new box must be formed

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A storage company needs to design a new storage box that has twice the volume of its largest box. Its largest box is 5 ft long, 4 ft wide, and 3 ft high. The new box must be formed      Log On


   

Question 960777: A storage company needs to design a new storage box that has twice the volume of its largest box. Its largest box is 5 ft long, 4 ft wide, and 3 ft high. The new box must be formed by increasing each dimension by the same amount. Find the increase in each dimension.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
v=xyz

2v=%28x%2Bk%29%28y%2Bk%29%28z%2Bk%29
More difficult this way, so instead choose a factor to increase each dimension the same amount, r.

2v=%28rx%29%28ry%29%28rz%29
2v=xyz%2Ar%5E3
r%5E3=2v%2F%28xyz%29
r%5E3=2v%2Fv
r%5E3=2
r=root%283%2C2%29
Again, r here is a factor for each dimension for how many times to increase them; NOT radius.

Thinking about the two different interpretations again, they are not the same. The intent of the description can very well be the ADDITION of a constant quantity to each dimension, and so the cubic expression using the three binomials can be the way to handle the question. Solving generally would be difficult, so you could or should try the actual given values, and assign k as the unknown amount to increase each dimension. Use then whatever polynomial function skills from College Algebra you are able.