# If the sum of two consecutive integers is 107, how do you find the integers?

Jan 31, 2016

The two integers are 53 and 54.

#### Explanation:

The key to this question is "two consecutive integers", because if they did not specify this info you would not be able to solve the problem.

Two consecutive integers can be represented by $n$ and $n + 1$. For example, if $n$ is $5$, then our 2 consecutive integers are $5$ and $5 + 1$, or $6$ - which makes sense, because $6$ comes right after $5$.

We are told these two integers sum to 107, which algebraically means this:

$n + \left(n + 1\right) = 107$

Now we have a 2-step equation, which we begin to solve by subtracting 1 from both sides and combining like terms:

$2 n = 107 - 1 = 106$

Now we divide both sides by 2 to get:

$n = \frac{106}{2} = 53$

Thus, $n = 53$ and $n + 1 = 53 + 1 = 54$. Our two consecutive integers that add to 107 are 53 and 54. 53 and 54 are definitely consecutive, and they definitely add to 107 - so I say we have an answer.