A homeowner is installing a swimming pool in his backyard. he want its length to be 4 feet longer than its width. then he wants to surround it with a concrete walkway 3 feet wide. if he can only afford 300 square feet of concrete for the walkway, what should the dimensions for the pool be?

1. You have that:

 - The homeowner want the length of the swimming pool to be 4 feet longer than its width. 
 - He wants to surround it with a concrete walkway 3 feet wide.
 - He can only afford 300 square feet of concrete for the walkway.

 2. Therefore, the tota area is:

 At=L2xW2

 L2 is the lenght of the walkway (L2=L1+3+3⇒L2=(W1+4+6)⇒L2=W1+10).
 W2 is the width of the walkway (W1+3+3⇒W2=W1+6)

 3. The area of the walkway is:

 A2=At-A1

 A2=300 ft²

 4. Therefore, you have that the width of the swimming pool is:

 A2=(W1+10)(W1+6)-(W1+4)(W1)
 300=(W1²+6W1+10W1+60)-(W1²+4W1)
 W1²+16W1+60-W1²-4W1-300=0
 12W1-240=0
 W1=240/12
 W1=20 ft

 5. And the length is:

 L1=W1+4
 L1=20+4
 L1=24 ft