Question

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Answer 1

The length of the shortest piece is
`1\textrm{ ft}`.

The length of the medium-sized piece is
`3\textrm{ ft}`.

The length of the longest piece is
`7\textrm{ ft}`.

Explanation:

The five-step method is GUESS method.

Given:

Length of copper wire,
`L=11\textrm{ ft}`

Length of longest piece is 6 feet longer than the shortest one.

Length of the medium-sized piece is 3 times the shortest one.

Unknown:

Length of longest, medium-sized and shortest pieces of wire.

Let the length of shortest piece be
`x` feet.

Therefore, the length of longest piece is equal to
`6+x`.

And, length of the medium-sized piece is equal to
`3x`.

Evaluate:

Sum of lengths of longest, medium-sized and shortest pieces of wire is equal to the total length of wire. So,

`6+x+x+3x=11\\5x+6=11\\5x=11-6\\5x=5\\x=(5)/(5)=1`

Substitute and Solve:

Now, we have,
`x=1`.

Substitute 1 for
`x` and solve for each sizes of wire pieces. This gives,

Length of shortest piece =
`x=1\textrm{ ft}`

Length of medium-sized piece =
`3x=3(1)=3\textrm{ ft}`

Length of longest piece =
`6+x=6+1=7\textrm{ ft}`

Therefore, the lengths of shortest, medium-sized, and longest pieces are
`1\textrm{ ft}`,
`3\textrm{ ft}` and
`7\textrm{ ft}` respectively.