Question

the dimensions of a rectangular field are 50m by 40m. A flower bed is prepared inside this field leaving a gravel path of a uniform width all around the flower bed. The total cost of laying the flower bed and gravelling the path at $30 and $20 per square metre respectively is $52000. Find the width of the gravel path.

Answer 1

Let x be the width of gravel path. 
Area of flower bed = (50-x)*(40-x) = x ^2 - 90x + 2000
Area of gravel path = total area - area of flowerbed
= 2000 - (x^2 -90x + 2000) = 90x -x^2
Cost of laying flower bed and gravel path is 52000
Flower bed cost = (x^2 - 90x + 2000)×30
Gravel path cost =( 90x - x^2)*20
(x^2-90x+2000)×30+(90x-x^2)×20=52000
x^2 (30-20)-90x (30-20)+60000=52000
10x^2-900x+8000=0
x^2-90x+800=0
x^2-10x-80x+800=0
x=10, 80
Width of the gravel path is 10m