<PRE><B>Question 153515</B>
A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet? 
:
Let x = width of the gravel path
:
Draw rough diagram of this labeling the garden as 18 by 13 and the width of the gravel path as x.
You will see the overall dimensions will be (2x+18) by (2x+13)
:
Overall area - garden area = gravel path area (required to be 516 sq/ft)
[(2x+18)(2x+13)] - (18*13) = 516
:
4x^2 + 62x + 234 - 234 = 516
; 
4x^2 + 62x - 516 = 0
Simplify, divide equation by 2:
2x^2 + 31x - 258 = 0
Factors to: 
(2x + 43)(x - 6) = 0
Positive solution
x = +6 ft is the width of the gravel path
:
:
Check solution: (overall = 30 by 25, added 12 ft)
(30*25) - (18*13) = 
750 - 234 = 516; confirms our solution</PRE>