SOLUTION: A Jewelery Box has a lenght that is 2 inches longer than the width and a height that is 1 inch smaller than the width. It has a volume of 140 cubic inches. What is the width? Pl

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Question 198164: A Jewelery Box has a lenght that is 2 inches longer than the width and a height that is 1 inch smaller than the width. It has a volume of 140 cubic inches. What is the width?
Please please help. I appreciate it!
Thank you very much
Found 3 solutions by josmiceli, vleith, Edwin McCravy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let w= the width in inches
w+%2B+2= the length
w+-+1= the height
Volume = length x width x height
w%2A%28w+%2B+2%29%2A%28w+-+1%29+=+140 in3
w%5E2+%2B+2w%29%2A%28w+-+1%29+=+140 in3
w%5E3+%2B+2w%5E2+-+w%5E2+-+2w+=+140
w%5E3+%2B+w%5E2+-+2w+=+140
factor out w
w%2A%28w%5E2+%2B+w+-+2%29+=+140
Factoring again:
w%2A%28w+%2B+2%29%28w+-+1%29+=+140
I'll say y+=+w%2A%28w+%2B+2%29%28w+-+1%29
I'll plot it and see where y+=+140 is
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+50%2C+x%5E3+%2B+x%5E2+-+2x%29+
It looks like w is going to be about 4
y%284%29+=+4%2A%284+%2B+2%29%2A%284+-+1%29
y%284%29+=+4%2A6%2A3
y%284%29+=+72
I'll try 5
y%285%29+=+5%2A7%2A4
y%285%29+=+140 bingo
The width is 5 inches

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
VolumeOfBox+=+Length+%2A+Width+%2A+Height
Length+=+Width+%2B+2
Height+=+Width+-+1
VolumeOfBox+=+Length+%2A+Width+%2A+Height
V+=+%28W%2B2%29+%2A+W+%2A+%28W+-1%29
140+=+%28w%5E2+%2B+2W%29+%2A+%28W-1%29
140+=+W%5E3+-+W%5E2+%2B+2W%5E2+-+2W
0+=+W%5E3+%2B+W%5E2+-+2W+-+140
No go here and plot that to find the zeros
http://www76.wolframalpha.com/input/?i=0+%3D+W^3+%2B+W^2+-+2W+-+140
Looks like 5 is the only real solution

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Edwin's solution:
A Jewelery Box has a length that is 2 inches longer than the width and a height that is 1 inch smaller than the width. It has a volume of 140 cubic inches. What is the width? 


Let the WIDTH=w

>>...length that is 2 inches longer than the width...<<

So LENGTH+=+WIDTH+%2B+2 or

   LENGTH+=+w+%2B+2

>>...a height that is 1 inch smaller than the width...<<

So HEIGHT+=+WIDTH+-+1 or

   HEIGHT+=+w+-+1



The formula for volume is

VOLUME=LENGTH%2AWIDTH%2AHEIGHT

>>...It has a volume of 140 cubic inches...<<

So we substitute 140 for VOLUME,
w%2B2 for LENGTH, and w-1 for HEIGHT:

140=%28w%2B2%29%2Aw%2A%28w-1%29

First we multiply the w by the %28w-1%29
by distributing:

140=%28w%2B2%29%2A%28w%5E2-w%29

Now we use FOIL on the right:

140=w%5E3-w%5E2%2B2w%5E2-2w 

140=w%5E3%2Bw%5E2-2w

0=w%5E3%2Bw%5E2-2w-140

w%5E3%2Bw%5E2-2w-140=0

The possible roots of this equation are the
factors of 140, which are

±1, ±2, ±4, ±5, ±10, ±14, ±28, ±35, ±70, ±140  

Start trying those with synthetic division and
sooner or later you'll get around to trying
x=5

5 | 1  1 -2 -140
  |    5 30  140
  --------------
    1  6 28    0

So the polynomial has been factored as

w%5E3%2Bw%5E2-2w-140=0

has been factored as

%28x-5%29%28x%5E2%2B6x%2B28%29=0

x-5-0 so x=5

x%5E2%2B6x%2B28=0 just give imaginary solutions.

So the WIDTH+=+w=5INCHES

Edwin