word problem help

lcase

New member
Joined
Sep 3, 2005
Messages
3
A rectangular flower bed is 10 ft longer thanits width. The flower bed is surrounded by a concrete walk that is 3 ft wide. If the area of the walk is 240, then what is the width of the flower bed?
 

Gene

Senior Member
Joined
Oct 8, 2003
Messages
1,904
Start by assigning variables to unknowns.
rectangular flower bed is 10 ft longer than it's width.
L=W+10
The flower bed is surrounded by a concrete walk that is 3 ft wide.
With the walk it is (L+2*3)by(W+2*3)
The area of the walk is the total area minus the area of the bed.
If the area of the walk is 240, then what is the width of the flower bed
(L+6)(W+6)-(L)(W)=240
Substitute W+10 for L in that last equation then solve for W.
 

soroban

Elite Member
Joined
Jan 28, 2005
Messages
5,588
Hello, lcase!

I assume you made a sketch . . .

A rectangular flower bed is 10 ft longer than its width.
The flower bed is surrounded by a concrete walk that is 3 ft wide.
If the area of the walk is 240, then what is the width of the flower bed?
Code:
     : 3 :    w+10   : 3 :
   - * - - - - - - - - - * 
   3 |                   |
   - |   * - - - - - *   |
     |   |           |   |
   w |  w|           |   | w+6
     |   |   w+10    |   |
   - |   * - - - - - *   |
   3 |                   | 
   - * - - - - - - - - - *
             w+16
(Area of walk) . = . (Total area) - (Area of garden)

. . . . . . . . 240 . = . (w + 6)(w + 16) - w(w + 10)


Simplify: . w<sup>2</sup> + 22w + 96 - w<sup>2</sup> - 10w .= .240

Then: . 12w = 144 . . ---> . . w = 12
 
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