Question

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Answer 1

Answer:

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 $7\textrm{ ft}$.

Step-by-step 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,

$6+x+x+3x=11\\5x+6=11\\5x=11-6\\5x=5\\x=\frac{5}{5}=1$

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.