SOLUTION: cookies are packaged in boxes whose width is 2 cm less than the length, and the height is 5 cm more than double the length. determine the dimensions of the box that will give a vol

Algebra ->  Volume -> SOLUTION: cookies are packaged in boxes whose width is 2 cm less than the length, and the height is 5 cm more than double the length. determine the dimensions of the box that will give a vol      Log On


   



Question 1087412: cookies are packaged in boxes whose width is 2 cm less than the length, and the height is 5 cm more than double the length. determine the dimensions of the box that will give a volume of 33 cm^3
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = the width in cm
+w+%2B+2+ = the length in cm
+2%2A%28+w+%2B+2+%29+%2B+5+ = the height in cm
---------------------------------------
+V+=+w%2A%28+w+%2B+2+%29%2A%28+2%2A%28+w+%2B+2+%29+%2B+5+%29+
+V+=+%28+w%5E2+%2B+2w+%29%2A%28+2w+%2B+4+%2B+5+%29+
+V+=+%28+w%5E2+%2B+2w+%29%2A%28+2w+%2B+9+%29+
+33+=+%28+w%5E2+%2B+2w+%29%2A%28+2w+%2B+9+%29+
+2w%5E3+%2B+4w%5E2+%2B+9w%5E2+%2B+18w+=+33+
+2w%5E3+%2B+13w%5E2+%2B+18w+-+33+=+0+
---------------------------------------
Let +w+=+1+
+2%2A1%5E3+%2B+13%2A1%5E2+%2B+18%2A1+-+33+=+0+
+2+%2B+13+%2B+18+-+33+=+0+
+33+-+33+=+0+
+w+%2B+2+=+3+
+2%2A%28+w+%2B+2+%29+%2B+5+=+2%2A3+%2B+5+
+2%2A%28+w+%2B+2+%29+%2B+5+=+11+
------------------------------
The dimensions are:
1 x 3 x 11
--------------------
I just guessed at +w=1+
There may be another way to do this, but
I dont know what that would be
You can get another opinion

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

cookies are packaged in boxes whose width is 2 cm less than the length, and the height is 5 cm more than double the length. determine the dimensions of the box that will give a volume of 33 cm^3
Let length be L
Then width = L - 2
Height = 2L + 5
We then get: L(L - 2)(2L + 5) = 33
According to the above equation, 3 factors have a PRODUCT of 33, and the only 3 INTEGRAL factors of 33 are: highlight_green%28matrix%281%2C4%2C+%221%2C%22%2C+%223%2C%22%2C+and%2C+11%29%29.