Arectangle garden is 80m by 60m. the new garden is 800m^2, how wide is the strip of lawn?

The border width is x
The sides are now (80 - 2x) + 2x, and (60 - 2x) + 2x
The area along one side is
2x^2 + x(80 - 2x) 
adding the other side doubles the area
so far,
4x^2 +2x(80 - 2x) 
now add in the areas left along the other two sides
2x(60-2x)
(This is hard to follow without a picture. Try drawing it)
The interior area is 800.
The whole area is 4800, so the difference is the border.
4800 - 800 = 4000
4x^2 + 2x(80 - 2x) + 2x(60 - 2x) = 4000
4x^2 + 160x - 4x^2 + 120x - 4x^2 = 4000

-4x^2 + 280x = 4000
-x^2 + 70x - 1000 = 0
multiply both sides by -1
x^2 - 70x + 1000 = 0
(x - 50)(x - 20) = 0
x = 50, 20 are the solutions
The answer can't be 50 because the width on both sides would be 
50 + 50 = 100, and that's greater than 80, the longest side.
That leaves x = 20 for the width of the strip.
check
4x^2 + 2x(80 - 2x) + 2x(60 - 2x) = 4000
4(20)^2 + 2*20(80 - 2*20) + 2*20(60 - 2*20) = 4000
4*400 + 40*40 + 40*20 = 4000
1600 +1600 + 800 = 4000
3200 + 800 = 4000
4000 = 4000