What two consecutive numbers are equal to 100?

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Answer 1 · 2016-06-06T21:00:20

No two consecutive integers sum to $100$ .

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

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.