Joseph gave 23 cards to each of his 15 students and had 12 cards left. How many cards did Joseph have at first? Give me reasons, before answering the question

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
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He gave 23 cards each to 15 students for a total of 23 * 15 = 345 cards. He has 12 cards left, so originally the number of cards was 345 + 12 = 357 cards. So the final answer is 357.