14. (15 points) Three students, $A$, $B$, and $C$, together folded 1000 paper cranes. It is known that $A$ folded 100 fewer cranes than 3 times the number $B$ folded, and $C$ folded 67 fewer cranes than $A$. How many cranes did $A$ fold?
【Analysis】Let $B$ fold $x$ paper cranes, then $A$ folds $3 x-100$ cranes, and $C$ folds $3 x-100-67$ cranes. Finally, according to “$A$, $B$, and $C$ three students together folded 1000 paper cranes”, set up an equation to solve.

【Solution】Solution: Let $B$ fold $x$ paper cranes, then $A$ folds $3 x-100$ cranes, and $C$ folds $3 x-100-67$ cranes.
$$
\begin{aligned}
x+3 x-100+3 x-100-67 & =1000 \\
7 x & =1000+100+100+67 \\
7 x & =1267 \\
x & =1267 \div 7 \\
x & =181 \\
3 x-100=3 \times 181-100 & =443 \text{ (cranes) }
\end{aligned}
$$

Answer: $A$ folded 443 paper cranes.
【Comment】The key is to identify the equal relationship between quantities, set one unknown as $x$, and express other unknowns with expressions containing $x$, then set up and solve the equation.