Let A be the area, L be the length and W be the width
"A rectangular garden is 4ft longer than it is wide" tells us L = W + 4
Also area = length x width, so A = LW,
"If the width is decreased by 1 ft., and the length is increased by 5ft., the area is increased by 15 square ft" tells us (W-1)(L+5) = A + 15.
Expanding out the brackets on the left hand side gives LW + 5W - L - 5 = A + 15. Since A = LW, this can be written as A + 5W - L - 5 = A + 15, and subtracting the A from both sides and adding 5 to both sides tells us 5W - L = 20 and substituting in L = W + 4 tells us 5W - (W + 4) = 20, which is the same as 5W - W - 4 = 20, which simplifies to 4W = 24 and therefore W = 6. Also L = W + 4 = 6 + 4 = 10.
So the garden is 6 feet wide and 10 feet long.
