Question

Find two consecutive integers whose sum is 67. Which of the following equations could be used to solve the problem?

Answer 1

The desired answer is probably that
  2x + 1 = 67
is the equation that can be used to solve the problem. In this case, x represents the smallest integer.

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I like to work problems in consecutive integers by considering their average. Here, it is 67/2 = 33.5. The two consecutive integers whose average is 33.5 are 33 and 34, the solution to the problem. For this, the first equation applies, where x is the value halfway between the two integers. (This answer (2x=67) would likely get marked wrong by your computer grading system.)