Question

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?

Answer 1

Step 1

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

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

Step 2

Find the length of each piece

`\begin{gathered} 3.5z+2.5z+z=35 \\ 7z=35 \\ z=5ft \end{gathered}`
`\begin{gathered} 3.5(5)=17.5ft \\ 2.5(5)=12.5ft \end{gathered}`

Answer;

`\begin{gathered} The\text{ longest piece=17.5ft} \\ Medium\text{ piece=12.5ft} \\ Shortest\text{ piece=5 ft} \end{gathered}`