Question

What two consecutive numbers are equal to 100?

Answer 1

No two consecutive integers sum to `100`.

`49` and `51` are the two consecutive odd integers whose sum is `100`.

Explanation:

Assuming the problem is asking what two consecutive integers sum to `100`, then there is no answer, as for any integer `n`, we have

`n+(n+1) = 2n+1`, which is odd, while `100` is even. Thus `2n+1 !=100` for any integer `n`.

If the problem is asking for two consecutive odd integers whose sum is `100`, we can find them as follows:

Let `n` be the lesser of the two odd integers, then we have

`n+(n+2) = 100`

`=> 2n+2 = 100`

`=> 2n = 98`

`=> n = 49`

Thus the two consecutive odd integers are `49` and `49+2=51`. Checking, we find that `49+51=100`, as desired.