16. A store received fewer than 600 but more than 500 plates. When they started arranging them in tens, they were short of three plates to make a complete number of tens, and when they started arranging them in dozens (12 plates), there were 7 plates left. How many plates were there?
16. If there were three plates short of a full number of tens, this means that, as with counting by dozens, there were 7 plates left. This means that the number of plates minus seven is divisible by both 10 and 12, i.e., by 60. Among the numbers less than 600 and greater than 500, only the number 540 is divisible by 60, so the number of plates was $540+7=547$