Question 215227
A 25-foot wire is to be cut so that the longer piece is one foot longer than 5 times the shorter piece.  find the length of each piece.


Step 1.  Let x be the shorter wire and 5x+1 be the longer wire.


Step 2.  x+5x+1=25    since adding the lengths of the two wires yields 25 ft as given by the problem statement.


Step 3.  Solving


{{{x+5x+1=25}}}


{{{6x+1=25}}}


{{{6x+1-1=25-1}}}


{{{6x=24}}}


{{{x=4}}}


With x=4, then 5x+1=21.  Note the two lengths add up to 25 feet.


Step 4. ANSWER: The length of the shorter wire is 4 feet and the longer wire is 21 feet.


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J