Question

If the sum of two consecutive integers is less than 83, how do you find the pair of integers with the greatest sum?

Answer 1

Two integers can only add to become another integer. The greatest integer less than `83` is `82`.

However, you can't have two consecutive integers adding up to give an even number, so we're going to have to pick the greatest odd number that's smaller than `83`, which is of course `81`.

So we are looking for two consecutive integers that add up to `81`. We are looking for a number `a` and the number after it `a+1`.
To do this, we can add them and set them equal to `83`.

`a + (a+1) = 83`
`2a = 82`

`a = 41`
`(a+ 1) = 42`
`41+42 = 83`

And that is good information, by we are looking for the biggest odd number that's smaller than `83` so we can subtract `1` from both numbers.

`(a-1) = 40`
`a = 41`
`40+41 = 81`