A grocery store has six wedges of cheese of different sizes, weighing 15, 16, 18, 19, 20, and 31 ounces. Five wedges are cheddar and one is mozzarella. Alice and Bob bought several wedges of cheddar. Alice bought two wedges and Bob bought twice as much by weight as Alice. Without resorting to trial and error, determine how much the mozzarella weighs.

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Source: Chris Long
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