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A man wants to cut three lengths from a single piece of board of length $91 \mathrm{~cm}$, the second length is to be $3 \mathrm{~cm}$ longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least $5 \mathrm{~cm}$ longer than the second?
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Let $x$ be the length of the shortest board, then $x+3$ is the second length and $2 x$ is the third length. Thus,
$\begin{aligned}
& x+(x+3)+2 x \Rightarrow 4 x+3 \leq 91 \\
\Rightarrow \quad & 4 x \leq 88 \Rightarrow x \leq 22
\end{aligned}$
According to the problem,
$2 x \geq(x+3)+5 \Rightarrow x \geq 8$
At least $8 \mathrm{~cm}$ long but not more than $22 \mathrm{~cm}$ long.
$\begin{aligned}
& x+(x+3)+2 x \Rightarrow 4 x+3 \leq 91 \\
\Rightarrow \quad & 4 x \leq 88 \Rightarrow x \leq 22
\end{aligned}$
According to the problem,
$2 x \geq(x+3)+5 \Rightarrow x \geq 8$
At least $8 \mathrm{~cm}$ long but not more than $22 \mathrm{~cm}$ long.
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