Question 1109220: --------------------------
A product packaging firm manufactures cardboard trays for holding 24 12 oz cans. The process begins with a rectangular piece of cardboard that is 5 inches longer than it wide. 2 inch squares are cut from each corner, and the flaps are folded up to form a tray. if the area of the bottom of the tray is 176 square inches, what are the original dimensions of the rectangle piece of cardboard.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A product packaging firm manufactures cardboard trays for holding 24 12 oz cans.
The process begins with a rectangular piece of cardboard that is 5 inches longer than it wide.
2 inch squares are cut from each corner, and the flaps are folded up to form a tray.
if the area of the bottom of the tray is 176 square inches, what are the original dimensions of the rectangle piece of cardboard.
:
Let w = the width of the cardboard
then
(w+5) = the length
:
2 in squares are cut from each corner, therefore each dimension is reduced by 4 in.
(w-4) = the width of the box
(w+1) = the length of the box
;
the area of the bottom
(w-4)(w+1) = 176
FOIL
w^2 + w - 4w - 4 = 176
w^2 + w - 4w - 4 - 176 = 0
w^2 - 3w - 180 = 0
You can use the quadratic formula a=1; b=-3; c=-180, but this will factor to:
(w-15)(w+12) = 0
The positive solution is what we want here
w = 15 in is the original width of the card board
then
15+5 = 20 in is the original length
:
:
Confirm this by finding the area of the bottom using these dimensions
Subtract 4 from each cardboard dimension
11 * 16 = 176
|
|
|
