SOLUTION: 4. The length of a rectangular bin is 2 more than its width and the height is 3 ft less than its width. Find the dimensions of the bin if its volume is 70f * t ^ 3

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Question 1176834: 4. The length of a rectangular bin is 2 more than its width and the height is 3 ft less than its width. Find the dimensions of the bin if its volume is 70f * t ^ 3
Found 3 solutions by josgarithmetic, MathLover1, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
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Are you trying to write this?

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The length of a rectangular bin is 2 feet more than its width, and the height is 3 feet less than its width. Find the dimensions of the bin if its volume is 70 ft^3.
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%28w%2B2%29%2Aw%28w-3%29=70
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w%28w%2B2%29%28w-3%29=70
w%2A%28w%5E2-w-6%29=70
w%5E3-w%5E2-6w-70=0

A graphing tool will show a real root of 5.

Dimensions: 7, 5, 2.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if the length L is 2ft more than its width W, we have
L=W%2B2ft
and if the height h is 3ft less than its width, we have
h=W-3ft
if its volume is 70ft%5E3, we have
L%2AW%2Ah=70....substitute L and h
%28W%2B2%29%2AW%2A%28W-3%29=70
W%5E3+-+W%5E2+-+6W=70
%28W+-+5%29+%28W%5E2+%2B+4+W+%2B+14%29+=+0
one real solution is W=5ft
then L=5ft%2B2ft=7ft and h=5ft-3ft=2ft

check the volume:
7ft%2A5ft%2A2ft=7ft%2A10ft+=70ft%5E3

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Informally....

70 = 2*5*7 so height 2, width 5, length 7

Algebraically....

x = width
x+2 = length
x-3 = height

The volume is 70:

x%28x%2B2%29%28x-3%29+=+70
x%5E3-x%5E2-6x+=+70
x%5E3-x%5E2-6x-70+=+0

What you do with that is up to you.

I would graph the function on a graphing calculator to find the x value that makes the function value 0.

Or I might solve the problem informally to find the width is 5, as shown above, and then verify that that answer gives the right volume.