Solution: If the unit price of the second prize is X yuan, the unit price of the first prize is (x+2) yuan, and the unit price of the third prize is (x- 1) yuan.

Then 9 (x+2)+17x+14 (x-1) ≥ 200 ....................... ①.

9(x+2)+ 17x+ 14(x- 1)≤250.......................②

There are solutions of ①x≥4.9 and ②x≤6. 1, that is, 4.9≤x≤6. 1, and the unit price of prizes is required to be an integer.

So x=5.

A: The unit price of the first prize is 7 yuan, the second prize is 5 yuan, and the third prize is 4 yuan.