SOLUTION: Brady wants to buy a rug for a room that is 10 ft wide and 15 ft long. He wants to leave a uniform strip of floor around the rug. He can afford to buy 100 ft2 . How wide of a bord

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Brady wants to buy a rug for a room that is 10 ft wide and 15 ft long. He wants to leave a uniform strip of floor around the rug. He can afford to buy 100 ft2 . How wide of a bord      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1141591: Brady wants to buy a rug for a room that is 10 ft wide and 15 ft long. He wants to leave a uniform strip of floor around the rug. He can afford to buy 100 ft2
. How wide of a border can he have? (The area in gray is 100 ft2). You will need to use the quadratic formula.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rug + the border must fit in the 10 x 15 room
Let +A+ = the area of the rug
Let +x+ = the width of the border
+A+=+%28+10+-+2x+%29%2A%28+15+-+2x+%29+
+A+=+150+-+30x+-+20x+%2B+4x%5E2+
+A+=+4x%5E2+-+50x+%2B+150+
+A+=+100+ ft2
+100+=+4x%5E2+-+50x+%2B+150+
+4x%5E2+-+50x+%2B+50+=+0+
+2x%5E2+-+25x+%2B+25+=+0+
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+2+
+b+=+-25+
+c+=+25+
+x+=+%28-%28-25%29+%2B-+sqrt%28+625+-+4%2A2%2A25+%29%29%2F4+
+x+=+%28+25+%2B-sqrt%28+625+-+200+%29%29%2F4+
+x+=+%28+25+-+sqrt%28+425+%29%29%2F4+
+x+=+%28+25+-+20.6155+%29%2F4+
+x+=+4.3845%2F4+
+x+=+1.0961+ ft is the minimum width of the border
------------------------
check:
+A+=+%28+10+-+2x+%29%2A%28+15+-+2x+%29+
+100+=+%28+10+-+2x+%29%2A%28+15+-+2x+%29+
+100+=+%28+10+-+2%2A1.0961+%29%2A%28+15+-+2%2A1.0961+%29+
+100+=+%28+10+-+2.1922+%29%2A%28+15+-+2.1922+%29+
+100+=+7.8078%2A12.8078+
+100+=+100.00074+
error due to rounding off
-----------------------------
get a 2nd opinion if needed