Question

Two consecutive odd integers have a sum of 48, what are the two odd integers?

Answer 1

23 and 25 together add to 48.

Explanation:

You can think of two consecutive odd integers as being value `x` and `x+2`. `x` is the smaller of the two, and `x+2` is 2 more than it (1 more than it would be even). We can now use that in an algebra equation:

`(x) + (x + 2) = 48`

Consolidate left side:
`2x + 2 = 48`

Subtract 2 from both sides:
`2x = 46`

Divide both sides by 2:
`x = 23`

Now, knowing that the smaller number was `x` and `x = 23`, we can plug `23` into `x+2` and get `25`.

Another way to solve this requires a bit of intuition. If we divide `48` by `2` we get `24`, which is even. But if we subtract `1` from it, and add `1` as well, we can get the two odd numbers that are next to it.