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A steel rod is 35 ft long must be cut into three pieces to fabricate the supports for a drill press. The longest piece is 3.5 times longer than the shortest piece the middle piece is 2.5 time longer than the shortest piece. How long is each piece?

Relax

Respuesta :

Step 1

Let us call the three pieces (long, short, and, medium): x,y,z. We get the following system of equations

[tex]\begin{gathered} 3.5z=x---(1) \\ 2.5z=y---(2) \\ x+y+z=35\text{ --\lparen3\rparen} \end{gathered}[/tex]

Step 2

Find the length of each piece

[tex]\begin{gathered} 3.5z+2.5z+z=35 \\ 7z=35 \\ z=5ft \end{gathered}[/tex][tex]\begin{gathered} 3.5(5)=17.5ft \\ 2.5(5)=12.5ft \end{gathered}[/tex]

Answer;

[tex]\begin{gathered} The\text{ longest piece=17.5ft} \\ Medium\text{ piece=12.5ft} \\ Shortest\text{ piece=5 ft} \end{gathered}[/tex]