Answer:
The length of the shortest piece is [tex]1\textrm{ ft}[/tex].
The length of the medium-sized piece is [tex]3\textrm{ ft}[/tex].
The length of the longest piece is [tex]7\textrm{ ft}[/tex].
Step-by-step explanation:
The five-step method is GUESS method.
Given:
Length of copper wire, [tex]L=11\textrm{ ft}[/tex]
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 [tex]x[/tex] feet.
Therefore, the length of longest piece is equal to [tex]6+x[/tex].
And, length of the medium-sized piece is equal to [tex]3x[/tex].
Evaluate:
Sum of lengths of longest, medium-sized and shortest pieces of wire is equal to the total length of wire. So,
[tex]6+x+x+3x=11\\5x+6=11\\5x=11-6\\5x=5\\x=\frac{5}{5}=1[/tex]
Substitute and Solve:
Now, we have, [tex]x=1[/tex].
Substitute 1 for [tex]x[/tex] and solve for each sizes of wire pieces. This gives,
Length of shortest piece = [tex]x=1\textrm{ ft}[/tex]
Length of medium-sized piece = [tex]3x=3(1)=3\textrm{ ft}[/tex]
Length of longest piece = [tex]6+x=6+1=7\textrm{ ft}[/tex]
Therefore, the lengths of shortest, medium-sized, and longest pieces are [tex]1\textrm{ ft}[/tex], [tex]3\textrm{ ft}[/tex] and [tex]7\textrm{ ft}[/tex] respectively.
