SOLUTION: Hello, I had some problems deriving a algebraic equation from this word problem... The volume of a rectangular box is 64ft^3. If the width is 3 times longer than the height, an

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Hello, I had some problems deriving a algebraic equation from this word problem... The volume of a rectangular box is 64ft^3. If the width is 3 times longer than the height, an      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 307047: Hello, I had some problems deriving a algebraic equation from this word problem...
The volume of a rectangular box is 64ft^3. If the width is 3 times longer than the height, and the length is 9 times longer than the height, find the dimensions of the box.
The formula for finding the volume of a retangular box is V=lwh.
I came up with 64=9l3wh, but no luck...and suggestions?
Thanks again, you all rock!
Alex
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since "the width is 3 times longer than the height, and the length is 9 times longer than the height", this means that W=3H and L=9H


V=LWH Start with the given volume formula.


64=%289H%29%283H%29H Plug in V=64 (the given volume) W=3H and L=9H


64=27H%5E3 Multiply


64%2F27=H%5E3 Divide both sides by 27.


root%283%2C64%2F27%29=H Take the cube root of both sides to isolate 'H'


4%2F3=H Take the cube root of 64%2F27 to get 4%2F3


So the height is H=4%2F3 ft. Simply plug this value into W=3H and L=9H to find the width and length respectively. I'll let you do this.