10. There are between 200 and 300 pencils that can be placed in red boxes of 10 or in blue boxes of 12 pencils each. When all the pencils were packed in red boxes, 7 pencils were left, and when packed in blue boxes, 3 pencils were short. How many pencils were intended for packing
Solution: $\left\{\begin{array}{ll}a=10 x+7=10(x+1)-3, & a+3 \mid 10, \\ a=12 y-3, & a+3 \mid 12,\end{array}\right\} \Rightarrow a+3 \mid 60$

Answer: $a=237, a=297$.

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