Beginning Algebra With Applications, Chapter 4, 4.1, Section 4.1, Problem 46

A 20-foot board is cut into two pieces. Twice the length of the shorter piece is 4 ft more than the length of the longer piece. Find the length of the shorter piece.

If we let $x$ and $y$ be the length of the shorter piece and the longer piece respectively, then we get


$
\begin{equation}
\begin{aligned}

x+y =& 20
\\
y =& 20-x \qquad \text{Equation 1}

\end{aligned}
\end{equation}
$


And

$2x = y+4 \qquad$ Equation 2

By substituting equation 1 to equation 2, we have


$
\begin{equation}
\begin{aligned}

2x =& (20-x) + 4
\\
2x =& 20-x+4
\\
2x+x =& 20+4
\\
3x =& 24
\\
x =& 8

\end{aligned}
\end{equation}
$


Thus, the length of the shorter piece is 4 ft.

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