Question 302389
Let's the walk way width be x 

The width including walk way = 12 + x + x  = 12 + 2x 
The length including walk way = 15 + x + x = 15 + 2x 

Area of the flower bed = 12*15 = 180 ft^2 
Area of the flower bed and walk way = (12+2x)*(15+2x) 

The difference of the two area is 90 ft^2 

Therefore: 

[(12+2x)*(15+2x)] - 180 = 90 
(180 + 24x + 30x + 4x^2) - 180 = 90
4x^2 + 54x - 90 = 0
2x^2 + 27x - 45 = 0 

Using the formular : {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
where a = 2 , b = 27 and c = -45 

x = 1.5 ft or - 15ft(N/A)

Answer: The width of the path way is 1.5ft