SOLUTION: Can someone please tell me how to find the dimensions of a box that has a volume of 504 cubic inches and its sides measure x, x+1 and x+2. Much appreciated!

Question 241197: Can someone please tell me how to find the dimensions of a box that has a volume of 504 cubic inches and its sides measure x, x+1 and x+2. Much appreciated!
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
x*(x+1)*(x+2) = 504

It's likely to be integers, so look for integer roots.
504 = 2*2*2*3*3*7 so it's likely a root will be 7 or a multiple of 7. Plus, the dimensions are 3 sequential numbers.
504 = 7*8*9, so that's the answer.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

,

So:

Using the Rational Root Theorem

http://en.wikipedia.org/wiki/Rational_root_theorem

To determine the possible rational roots. You can also use your graphing calculator to find a root of the equation. You could also realize that x + 1 will probably be very close to the cube root of 504. Use your calculator to find a numeric approximation of cube root of 504, then take the nearest integer as x + 1.

John

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