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Let the cost of one puzzle be x and the cost of one piece of candy be y.
From the given information, we can set up the following equations:
2x + y = 8.00
x + y = 4.50
By solving the second equation for y, we get y = 4.50 - x.
Substitute this expression for y into the first equation:
2x + 4.50 - x = 8.00
x + 4.50 = 8.00
x = 3.50
Therefore, each puzzle costs $3.50.