SOLUTION: I really would appreciate your help understanding problems like the one below: Marie Mulroney has a rectangular board 12 inches by 16 inches around which she wants to put a unif

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I really would appreciate your help understanding problems like the one below: Marie Mulroney has a rectangular board 12 inches by 16 inches around which she wants to put a unif      Log On


   

Question 1111156: I really would appreciate your help understanding problems like the one below:
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.
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There is a border on both sides of the 12 in
side, so that each side is +12+%2B+2x+ in long
Also, there is a border on each side of the
16 in side, so this side is +16+%2B+2x+ in long
-------------------------------------------
Add up the inside area and the ares of the border.
+12%2A16+%2B+128+=+192+%2B+128+
+192+%2B+128+=+320+ in2
----------------------------
Now I can say:
+%28+12+%2B+2x+%29%2A%28+16+%2B+2x+%29+=+320+
+192+%2B+32x+%2B+24x+%2B+4x%5E2+=+320+
+4x%5E2+%2B+56x+-+128+=+0+
+x%5E2+%2B+14x+-+32+=+0+
+%28+x+%2B+16+%29%2A%28+x+-+2+%29+=+0+ ( by observation )
+x+=+2+ ( can only use the positve result )
The width of the border is 2 in
-----------------------------------
check:
+%28+12+%2B+2%2A2+%29%2A%28+16+%2B+2%2A2+%29+=+320+
+16%2A20+=+320+
+320+=+320+
OK

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
If you want to see other similar solved problems,  look into the lessons
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
    - Problems on a circular pool and a walkway around it
in this site.