Since the high temperature is $16$ degrees higher than the low temperature, it follows that the average of the two temperatures, which lies halfway between the high and low temperatures, must be $8$ degrees higher than the low temperature and $8$ degrees lower than the high temperature. Thus, if the average is $3^\circ,$ then the low temperature is $3^\circ - 8^\circ = \boxed{-5^\circ}.$
On a particular January day, the high temperature in Lincoln, Nebraska, was $16$ degrees higher than the low temperature, and the average of the high and the low temperatures was $3\,^\circ$. In degrees, what was the low temperature in Lincoln that day?
{'answer': '-5^\\circ', 'subject': 'Prealgebra', 'level': 4, 'unique_id': 'test/prealgebra/1249.json'}