Find two conesecutive integers whose sum is 45

First, let's declare that the average of the two integers would be 22.5. Using this, we are going to try and find two consecutive integers that have an average of 22.5. We can start to work outward from this average and see what integers work.

Instantly, we can test the integers 22 and 23. They have an average of 22.5 and sum to 45. Thus, they are our answer.

Think of one of our integers that we don't know as N. If we add one more to N, we get N + 1. So let's say N and N + 1 are the two numbers. We are told they add up to 45.

N + (N + 1) = 45 The two numbers are N, N + 1, and add to 45.

2N + 1 = 45 Add the N terms on the left side

2N = 44 Subtract 1 on both sides

N = 22 Divide both sides by 2

So N = 22. When we add one to it, we get 23. A check shows that 22 and 23 are consecutive and add to 45.

Thus, the two integers are 22 and 23.