Answer:
The length of the shorter piece is [tex]5\textrm{ ft}[/tex].
The length of the longer piece is [tex]11\textrm{ ft}[/tex].
Step-by-step explanation:
The five-step method is GUESS method.
Given:
Length of steel beam, [tex]L=16\textrm{ ft}[/tex]
Length of longer piece is 1 foot longer than twice the shorter one.
Unknown:
Length of longer and shorter pieces of beam.
Let the length of shorter piece be [tex]x[/tex] feet.
Therefore, the length of longer beam is equal to [tex]1+2x[/tex]
Evaluate:
Sum of lengths of longer and shorter pieces of beam is equal to the total length of beam. So,
[tex]x+1+2x=16\\3x+1=16\\3x=16-1\\3x=15\\x=\frac{15}{3}=5[/tex]
Substitute and Solve:
Now, we have, [tex]x=5[/tex].
Substitute 5 for [tex]x[/tex] for the lengths of shorter and longer pieces and solve for each. This gives,
Length of shorter piece = [tex]x=5\textrm{ ft}[/tex]
Length of longer piece = [tex]1+2x=1+2(5)=1+10=11\textrm{ ft}[/tex]
Therefore, the lengths of shorter and longer pieces are [tex]5\textrm{ ft}[/tex] and [tex]11\textrm{ ft}[/tex] respectively.
