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To solve this problem, we need to calculate the weight of the palettes and then add it to the weight of the cab and trailer.
The weight of each palette is 1,200 pounds.
The number of palettes is 31.
So the total weight of the palettes is 1,200 pounds * 31 = 37,200 pounds.
To find the total weight of the tractor trailer, we add the weight of the cab (7,600 pounds), the weight of the trailer (10,800 pounds), and the weight of the palettes (37,200 pounds).
Total weight = 7,600 pounds + 10,800 pounds + 37,200 pounds = 55,600 pounds.
Therefore, the total weight of the tractor trailer when there are 31 palettes on the trailer is 55,600 pounds.