SOLUTION: Ref. Question 1055935: A driveway is paved with concrete with enough remaining for 200 sq. ft. of surface. The remaining concrete is for a walkway around a flower garden 20 ft.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Ref. Question 1055935: A driveway is paved with concrete with enough remaining for 200 sq. ft. of surface. The remaining concrete is for a walkway around a flower garden 20 ft.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1056062: Ref. Question 1055935:
A driveway is paved with concrete with enough remaining for 200 sq. ft. of surface. The remaining concrete is for a walkway around a flower garden 20 ft. by 15 ft. Determine width of walkway which can be placed with remainder. Thanks.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the walkway = +x+
My equation for the area of walkway is:
+2x%2A15+%2B+2x%2A%28+20+%2B+2x+%29+=+200+
+30x+%2B+40x+%2B+4x%5E2+=+200+
+4x%5E2+%2B+70x+-+200+=+0+
+2x%5E2+%2B+35x+-+100+=+0+
Use quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+35+
+c+=+-100+
-------------------
+x+=+%28-35+%2B-+sqrt%28+35%5E2-4%2A2%2A%28-100%29+%29%29+%2F+%282%2A2%29+
+x+=+%28-35+%2B-+sqrt%28+1225+%2B+800+%29%29+%2F+4+
+x+=+%28+-35+%2B+sqrt%28+2025+%29+%29+%2F+4+
+x+=+%28+-35+%2B+45+%29+%2F+4+
+x+=+10%2F4+
+x+=+5%2F2+
---------------
The width of the walkway is 2.5 ft
-----------------
check:
+4x%5E2+%2B+70x+-+200+=+0+
+4%2A2.5%5E2+%2B+70%2A2.5+-+200+=+0+
+4%2A6.25+%2B+175+-+200+=+0+
+25+%2B+175+-+200+=+0+
+200+-+200+=+0+
OK