Students were asked to find three consecutive whole numbers

Students were asked to find three consecutive whole numbers whose sum is 393. One student wrote the equation x + (x + 1) + (x + 2) = 393. Another wrote (x -1) + x + (x + 1) = 393. Can either approach work to find the answer to the question? Explain why or why not.

Solution

Students were asked to find three consecutive whole numbers whose sum is 393. One student wrote the equation x + (x + 1) + (x + 2) = 393. Another wrote (x -1) + x + (x + 1) = 393. Either approach will be adequate enough in finding the answer to the question as we can assume either the 1^st number to be x, in which case, the 2^nd and the 3^rd numbers will be x+1and x+2 respectively, or, we can assume the 2^nd number to be x in which case, the 1^st number and the 3^rd number will be x-1 and x+1 respectively. In either case, the answer will be 130,131 and 132.