Question 1147587: A rectangular piece of cardboard is 5 inches longer than it is wide. Three-inch squares are cut out of each corner and the resulting flaps are turned up and taped to form an open box. If the volume of the resulting box is 18 cubic inches, what were the original dimensions of the piece of cardboard?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Without algebra....
The volume is 18; and the height is 3, because the corners cut out of the piece of cardboard are 3x3 squares.
Since volume is length times width times height, the product of the length and width is 18/3 = 6.
If the original piece of cardboard is 5 inches longer than it is wide, then after the square pieces are cut off of each corner the bottom of the box will be 5 inches longer than it is wide.
So we need two numbers that differ by 5 whose product is 6; those numbers, trivially, are 6 and 1.
So the bottom of the box is 6x1 inches; since 3 inches in each direction were cut off of each corner of the original piece of cardboard, the dimensions of the original piece of cardboard were (6+6)x(1+6) = 12x7 inches.
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