Question 302419
Let's the stone border width be x
The width including stone border = 6 + x + x = 6 + 2x
The length including stone boarder = 15 + x + x = 15 + 2x
Area of the garden = 6*15 = 90 yards^2
Area of the garden and stone border = (6+2x)*(15+2x)
The difference of the two area is 100 yards^2
Therefore:
[(6+2x)*(15+2x)] - 90 = 100
(90 + 12x + 30x + 4x^2) - 90 = 100
4x^2 + 42x - 100 = 0
2x^2 + 21x - 50 = 0
Using the formular : {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
where a = 2 , b = 21 and c = -50
x = 2 yard or - 12.5 yards(N/A)
Answer: The width of the path way is 2 yards.