SOLUTION: 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.

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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.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B5x%2B1=25

6x%2B1=25

6x%2B1-1=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