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Based on the proportion of cheese pizza slices to total slices sold, we can set up a ratio:
3 slices of cheese pizza / 20 total slices = x slices of cheese pizza / 5680 total slices
Cross multiplying, we get:
3 * 5680 = 20x
17,040 = 20x
x = 852
Therefore, if the pizza parlor sells 5,680 total slices in a week, they are predicted to sell 852 slices of cheese pizza.