SOLUTION: I am having a difficult time with a word problem, could you please help me how to solve it? A factory needs a box that has a volume of 6 cubic feet. The width should be 1 inch

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Question 582525: I am having a difficult time with a word problem, could you please help me how to solve it?
A factory needs a box that has a volume of 6 cubic feet. The width should be 1 inch less than the height and the length should be 3 inches greater than the height. Approximate what the dimensions of the box should be?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +h+ = height of box
given:
width = +h+-+1+
length = +h+%2B+3+
Volume = width x length x height
+6+=+h%2A%28+h+-+1+%29%2A%28+h+%2B+3+%29+
+6+=+h%2A%28+h%5E2+-+h+%2B+3h+-+3+%29+
+6+=+h%2A%28+h%5E2+%2B+2h+-+3+%29+
+6+=+h%5E3+%2B+2h%5E2+-+3h+
+h%5E3+%2B+2h%5E2+-+3h+-+6+=+0+
The only way I know to solve this
is to carefully plot it ( or use a program )
Here's the plot:
+graph%28+400%2C+400%2C+-4%2C+4%2C+-10%2C+10%2C+x%5E3+%2B+2x%5E2+-+3x+-+6+%29+
It looks like +h+=+1.8+ approximately
Then the width is
+h+-+1+=+.8+
The length is
+h+%2B+3+=+4.8+
The volume would be
+1.8%2A.8%2A4.8+=+6.912+ (too much)
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If I say +h+=+1.75+
width = +.75+
length = +4.75+
+1.75%2A.75%2A4.75+=+6.23+
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I'm guessing that +h+=+1.7+
The dimensions are
1.7 x .7 x 4.7
( very close )