10. In the packaging workshop, there are 2 types of boxes: one for 20 parts and one for 27 parts. A batch of parts between 500 and 600 pieces has arrived for packaging. When the parts are packed in the first type of box, 13 parts are left unpacked, and when packed in the second type of box, 7 spaces are left unfilled. How many parts were in the batch?
Solution: ${ }^{a=20 x+13=20(x+1)-7,} a+7 \vdots 20 ; a+7 \vdots 27, \Rightarrow a+7 \vdots 540$.

$$
a=27 x-7
$$

Answer: $a=533$.

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