SOLUTION: A Standard rectangular shipping box has a length which is 3.5 inches more than its height. The width is 3 inches less than its height. What is the height of the box if its volume i

Algebra ->  Rational-functions -> SOLUTION: A Standard rectangular shipping box has a length which is 3.5 inches more than its height. The width is 3 inches less than its height. What is the height of the box if its volume i      Log On


   

Question 1147958: A Standard rectangular shipping box has a length which is 3.5 inches more than its height. The width is 3 inches less than its height. What is the height of the box if its volume is 561 cubic inches?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


height: x
width: x-3
length: x+3.5

volume = length * width* height

x%28x-3%29%28x%2B3.5%29+=+561

Probably solve using a graphing calculator....

Or, if you are really good with mental arithmetic, solve by trial and error:

561 = 11*51 = 3*11*17

The problem says two of the dimensions differ by 3; and the factors 11 and 17 differ by 6. That might lead you to

3*11*17 = 12*(11/2)*(17/2)

And those dimensions satisfy the conditions of the problem:
x = 17/2 = 8.5
x-3 = 11/2 = 5.5
x+3.5 = 17/2+7/2 = 24/2 = 12

ANSWER: the height of the box is x = 8.5 inches.