SOLUTION: 45 INCH BOARD IS TO BE CUT INTO THREE PIECES SO THAT THE SECOND PIECE IS 3 TIMES AS LONG AS THE FIRST PIECE AND THE THIRD PIECE IS 5 TIMES AS LONG AS THE FIRST PIECE. IF X REPRESE

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Question 182379This question is from textbook aLGEBRA A COMBINED APPROACH
: 45 INCH BOARD IS TO BE CUT INTO THREE PIECES SO THAT THE SECOND PIECE IS 3 TIMES AS LONG AS THE FIRST PIECE AND THE THIRD PIECE IS 5 TIMES AS LONG AS THE FIRST PIECE. IF X REPRESENTS THE LENGTH OF THE FIRST PIECE, FIND THE LENGTHS OF ALL THREE PIECES This question is from textbook aLGEBRA A COMBINED APPROACH

Answer by MathGuyJoe(20) About Me  (Show Source):
You can put this solution on YOUR website!
First off, try to avoid typing in all caps -- it's difficult to read and some folks treat it as shouting.


Let x = length of 1st piece
Let y = length of 2nd piece
Let z = length of 3rd piece


We know the total length of the board is 45, so:
Equation 1: +x+%2B+y+%2B+z+=+45+


We also know that the 2nd piece is 3 times the length of the 1st piece:
Equation 2: +y+=+3x+


We also know that he 3rd piece is 5 times the length of the 1st piece:
Equation 3: +z+=+5x+


Now we can substitute the values from equations 2 and 3 into equation 1:
Equation 1: +x+%2B+y+%2B+z+=+45+
Substitute: +x+%2B+%283x%29+%2B+%285x%29+=+45+
Solving for x gives us:
+9x+=+45+
++x+=+5+


Substituting this value back into equations 2 and 3 will give us the values of y and z:
Equation 2: +y+=+3x+
Substitute: +y+=+3%285%29+
+y+=+15+


Equation 3: +z+=+5x+
Substitute: +z+=+5%285%29+
+z+=+25+


So the final answers are x = 5, y = 15 and z = 25.