a 44-foot of wire is cut into three pieces so that the second piece is four times the length of the first piece, and the third piece is six feet less than five times the length of the first piece. find the length of the pieces
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Notice how the problem keeps referencing all the lengths in terms of "the first piece". It's usually a good idea to say "ok, let the length of first piece = X."
First piece = X
Second piece = "four times the length of ... X"
Third piece = "Six feet less than five times the length of ... X"
Now, the WHOLE wire is 44 ft long. So add up those three parts and set it equal to 44. You will have an equation with X + constant = 44.
From there, it's a bit of algeba, and that'll give you the answer for X, which we must remember is the length of THE FIRST PIECE.
You still have to take "X" and figure out what the other pieces are. (multiply by four... multiply by 5 and add six feet.)
Hope this helps!