A 36 – foot-long rope is cut into three pieces.  The first piece of ribbon is half as long as the second piece of ribbon. The third piece is 1 foot longer than twice the length of the second piece of ribbon.  How long is the longest piece of ribbon? 

the pieces are x,y,z length the sum is 36 x+y+z=36 x is first, y is 2nd, z is 3rd x=y/2 z=1+2y subsitute x+y+z=36 (y/2)+y+1+2y=36 (y/2)+3y+1=36 minus 1 both sides (y/2)+3y=35 times both sides by 2 y+6y=70 7y=70 divide both sides by 7 y=10 the 2nd piece of ribbon is 10ft