In a school chess tournament, there are five students ranked from first to fifth place. The prize for the first place is $100, which is $40 more than the prize for the second place. The prize for the second place is $20 more than the prize for the third place. The prize for the third place is $10 more than the prize for the fourth place. The prize for the fifth place is half of the prize for the fourth place. Calculate the total prize money given out in the tournament. Let's think step by step and output the final answer within \boxed{}.
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