Question

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Answer 1

Answer:

The length of the shorter piece is $5\textrm{ ft}$.

The length of the longer piece is $11\textrm{ ft}$.

Step-by-step explanation:

The five-step method is GUESS method.

Given:

Length of steel beam, $L=16\textrm{ ft}$

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 $x$ feet.

Therefore, the length of longer beam is equal to $1+2x$

Evaluate:

Sum of lengths of longer and shorter pieces of beam is equal to the total length of beam. So,

$x+1+2x=16\\3x+1=16\\3x=16-1\\3x=15\\x=\frac{15}{3}=5$

Substitute and Solve:

Now, we have, $x=5$.

Substitute 5 for $x$ for the lengths of shorter and longer pieces and solve for each. This gives,

Length of shorter piece = $x=5\textrm{ ft}$

Length of longer piece = $1+2x=1+2(5)=1+10=11\textrm{ ft}$

Therefore, the lengths of shorter and longer pieces are $5\textrm{ ft}$ and $11\textrm{ ft}$ respectively.