The reciprocal of an integer plus the reciprocal of two times the integer plus two equals 23 Find the integer?

This question can be expressed algebraically as: (1/n) + (1/(2n)) + 2 = 23, (1/n) + (1/(2n)) =21, ((1+2)/(2n)) = 21, (3/(2n)) = 21, or 2n = (3/21), 2n = (1/7), so n = (1/14). This, by the way, is an elementary algebraic proof that the solution to the above relation is (1/14). Anyway, to answer the question, reread the question: "[What integer is such that] the reciprocal of the integer...". notice, the reciprocal of (1/14) is 14, which is the integer in question! ^_^