Question

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?

Answer 1

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

Answer 2

The length of the longest piece of the ribbon is:

21 feet

Explanation:

It is given that:

A 36 – foot-long rope is cut into three pieces.

Let the length of first piece of ribbon= x

The length of second piece of ribbon= 2x

( since, the first piece of ribbon is half as long as the second piece of ribbon)

Also,

The third piece is 1 foot longer than twice the length of the second piece of ribbon.

i.e. the length of third piece is: 2(2x)+1

i.e.

The length of third piece= 4x+1

Hence, we have:

sum of the length of three pieces= 36

i.e.

x+2x+4x+1=36

i.e.

7x+1=36

i.e.

7x=36-1

i.e.

7x=35

On dividing both side of the equation by 7 we have:

x= 5

Hence, the length of first piece= 5 feet

Length of second piece= 2(5)=10 feet

and Length of Third piece = 2(10)+1= 21 feet