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) (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:
We also know that the 2nd piece is 3 times the length of the 1st piece:
Equation 2:
We also know that he 3rd piece is 5 times the length of the 1st piece:
Equation 3:
Now we can substitute the values from equations 2 and 3 into equation 1:
Equation 1:
Substitute:
Solving for x gives us:
Substituting this value back into equations 2 and 3 will give us the values of y and z:
Equation 2:
Substitute:
Equation 3:
Substitute:
So the final answers are x = 5, y = 15 and z = 25.
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