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