SOLUTION: A 94 ft. rope is cut into three pieces. The second piece is 2 feet longer then the shortest piece. The third is 4 feet less then twice the shortest piece. How long is each piece?

Question 261765: A 94 ft. rope is cut into three pieces. The second piece is 2 feet longer then the shortest piece. The third is 4 feet less then twice the shortest piece. How long is each piece?
Answer by Stitch(470) (Show Source): You can put this solution on YOUR website!
Setup:
---------
Notice that each length is given in respect to the shotest piece.
Let A = the length of the shortest piece
Let B = the length of the second piece
Let C = the length of the third piece
Equation 1:
Equation 2:
Equation 3:

Solution:
---------------
Since we know what B and C equal in terms of A, we can substitute the values into equation 3
Equation 3:

Combine like terms

Add 2 to both sides

Divide both sides by 4

Now we can find the other lengths by replacing A with 24 in equations 1 & 2
Equation 1:

Equation 2:

Check the answers:
------------------
We can check the answers by placing them back into eqaution 3
Equation 3:

RELATED QUESTIONS
A 257 foot rope is cut into 4 pieces. The second piece is 3 feet longer than twice the... (answered by ankor@dixie-net.com)

a rope that is 33 feet long is cut into three pieces one piece is twice as long as the... (answered by josmiceli)

A piece of rope is 497 feet long. It is cut into 3 pieces. The first three times as... (answered by mananth)

a 120 foot long rope is cut into 3 pieces. the first piece of rope is twice as long as... (answered by RAY100)

A 60 feet long piece of string is cut into 3 pieces. The second piece is twice as long as (answered by hinaahsan)

I am needing help in setting up this equation: A 96 ft rope is cut into 4 pieces. The... (answered by ikleyn,VFBundy,solver91311,Theo,MathTherapy)

A 45 foot rope is to be cut into 3 pieces. The second piece must be twice as long as the... (answered by nerdybill,rapaljer)

zach had a rope that was 15 feet long. he cut it into 3 pieces. the first piece is 3.57... (answered by JulietG)

A 64 inch board is cut into 3 pieces. The second piece is three times as long as the... (answered by Nate)