A36 – 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 length of the longest piece of the ribbon is:

                          21 feet

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

answer: a and b

step-by-step explanation:

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step-by-step explanation: