# word problem help

#### lcase

##### New member
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
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
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