SOLUTION: Marie Mulroney has a rectangular board 12 inches by 16 inches around which she wants to put a uniform border of shells. If she had enough shells for a border whose area is 128 squa

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Question 853664: Marie Mulroney has a rectangular board 12 inches by 16 inches around which she wants to put a uniform border of shells. If she had enough shells for a border whose area is 128 square inches, determine the width of the border.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Marie Mulroney has a rectangular board 12 inches by 16 inches around which she wants to put a uniform border of shells.
If she had enough shells for a border whose area is 128 square inches, determine the width of the border.
:
Find the area of the of the board: 12 * 16 = 192 sq inches
then
128 + 192 = 320 sq/in, area of the board and the border
:
Let x = the width of the border
:
(x+12)(x+16) = 320
FOIL
x^2 + 16x + 12x + 192 - 320 = 0
x^2 + 28x - 128 = 0
Factors to
(x+32)(x-4) = 0
The positive solution is all we want here
x = 4 inches is the border width.
:
;
Check this, find the find the total area with 4" added
16 * 20 = 320 sq/in