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Let's assume that the cost of one puzzle is x and the cost of one piece of candy is y.
From the given information, we can form two equations:
2x + y = 8.00
x + y = 4.50
Now we can solve these two equations simultaneously:
Subtract the second equation from the first:
2x + y - x - y = 8.00 - 4.50
x = 3.50
Therefore, the cost of one puzzle is $3.50.