Find three consecutive odd integers such that the sum of those integers is 111. What are the numbers?

Answer 1

35, 37, 39.

First step is to think about what the question is indirectly asking for. If the sum of the numbers is 111, then the average for each of the 3 numbers will be 37, since 111/3 is 37.

Second step is to come up with a valid solution for that grouping. Including the set's average makes sense to simplify the math and since 37 is an odd integer. For a set of three numbers, including the number that is the set average means that the other two numbers should have exactly the same absolute difference with the average. In this case, the average is 37, so one number would be 37+X and the other 37-X. And the qualifier, consecutive odd integers lets you know that the difference, or X, needs to be 2.

Final step is to substitute in 2, leaving you with 37-2, which is 35, 37, and 37+2, which is 39. So the answer is 35, 37, and 39.

Answer 2

To solve this problem, we can set up an equation. If we call the first integer x, then the next integer would be x+2, and the third would be x+4. We know that all three added together equals 111, so we can write the equation

x + x + 2 + x + 4 = 111

By combining like terms, we get

3x + 6 = 111

Subtracting 6 from both sides gives us

3x = 105

Finally we divide by 3 to solve for x

x = 35

Plugging back in for our other two integers, we see that the three integers are 35, 37, and 39