[Math help] The length of a rectangular piece of tin is twice its width. A two-inch square is cut from each...
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[Math help] The length of a rectangular piece of tin is twice its width. A two-inch square is cut from each...

[From: ] [author: ] [Date: 12-07-04] [Hit: ]
volume = length * width * height.A negative width makes no sense so discard w = -1,......
corner so that a box may be formed by folding up the sides. If the box has a volume of 60 cubic inches, what was the width of the original piece of tin?

a) 7''
b) 6''
c) 10''
d) 14''
e) 15''

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Let w = original width. This makes the original length = 2w.
After the cuts, the width changes to w - 4 and the length changes to 2w - 4. The height is 2.
volume = length * width * height.
60 = (2w - 4)(w - 4)2
30 = (2w - 4)(w - 4)
30 = 2w^2 - 12w + 16
15 = w^2 - 6w + 8
0 = w^2 - 6w - 7
0 = (w - 7)(w + 1)
w = 7 or w = -1
A negative width makes no sense so discard w = -1, leaving just
w = 7in
1
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