How do you solve math problems like "the sum of two consecutive ODD integers"?

Question

like it says the sum of two consecutive ODD integers is 56. find the integers. how do you do that problem?

thanks!

Answer 1

The two consecutive integers that add to 56 are 27 and 29.

Let A(n) = n - 1, B(n) = n + 1, and C(n) = A(n) + B(n) = 56. Consider the fact that 2*n = any even integer for any integer n. Then, because 56 is even, 2*n = 56, which implies that n = 28. Now, A(28) = 27, B(28) = 29; hence, C(28) = 27 + 29, which is true since n is between two consecutive odd integers that add to 56.