SOLUTION: A club swimming pool is 17 ft wide and 33 ft long. The club members want an exposed aggregate border in a strip of uniform width around the pool. They have enough material for 600

Let w be a uniform strip width.


Then the outside (exterior) dimensions of the larger rectangle are 17+2w and 33+2w.


The area of the larger rectangle is (17+2w)*(33+2w).


The equation for the area of the border strip around the pool is

(17+2w)*(33+2w) - 17*33 = 600,   or

34w + 66w + 4w^2 = 600,

4w^2 + 100w - 600 = 0  ====>

w^2 + 25w - 150 = 0,

Factor left side:

(w+30)*(w-5) = 0

The roots are w= -30  and  w= 5.


Only positive root makes sense:  w = 5 ft.


Answer.  The strip should be 5 ft wide.