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''
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
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