Let the base of the ladder be x ft and the extension be y ft.
"when fully extended, a ladder is 28 feet in length."
means: x+y=28
"the extension is 4 feet shorter than the base"
means: y=x-4, that is x-y = 4, (taking y to the side of x, and -4 to the other side of x and y)
thus, we have the system of equations:
1) x+y= 28
2) x-y=4
adding the 2 equations, we have:
(x+y)+(x-y)=28+4
2x=32
x=32/2=16
x+y=28, so 16+y=28, thus y=12
Answer: Base: 16, Extension 12
