Solving Equations: Word Problems - Examples & Practice

Calvin was asked to evaluate $37 + 31 \times a$ for some number $a$. Unfortunately, his paper was tilted $45$ degrees, so he mistook multiplication for addition (and vice versa) and evaluated $37 \times 31 + a$ instead. Fortunately, Calvin still arrived at the correct answer while still following the order of operations. For what value of $a$ could this have happened?

Source: $2012-2013$ Fall Online Math Open