The sum of three consecutive integers is 45. What is the middle number?

Answer 1

Let's say the first number is x.

Because these are consecutive integers, the next number will just be 1 more than x, or x + 1.

Similar for the third number, it will be 1 more than the second, so (x + 1) + 1 = x + 2. Another way to think about this is it's two more than the first number, x. So now we have three unknown numbers that's we'll represent with the following:

x

x + 1

x + 2

Now we know the sum of these is 45, so we can set up an equation by adding all three of our unknown numbers and setting them equal to 45.

x + (x + 1) + (x + 2) = 45

x + x + 1 + x + 2 = 45

3x + 3 = 45

3x = 42

x = 14

If any part of that didn't make sense, feel free to ask questions by replying to this answer. But wait, we're not done here. We only solved for the first number, x. It's important to remember what the question is asking, and the question asked for the middle number, which was 1 more than x, or x + 1. Now that we know x = 14, let's add one to it.

x + 1 = 14 + 1 = 15.

Now we have our middle number, which is 15. You can always check your answer by adding 14 + 15 + 16 = 45. Whoo!