# Two consecutive integers have a sum of 113. How do you find the integers?

##### 2 Answers
Nov 17, 2016

The two numbers are $56$ and $57$.

#### Explanation:

Let the two consecutive integers be $x$ and $\left(x + 1\right)$. Therefore:

$x + \left(x + 1\right) = 113$

Open the brackets and simplify.

$x + x + 1 = 113$

$2 x + 1 = 113$

Subtract $1$ from both sides and then divide both sides by $2$.

$2 x = 112$

$x = 56$

$\therefore \left(x + 1\right) = 57$

Nov 17, 2016

The consecutive integers are 56 and 57.

$56 + 57 = 113$

#### Explanation:

Define the two integers with variables first.

Consecutive numbers are those which follow each other in sequence. 12, 13, 14, 15 ....

They always differ by 1,

If we let the first integer be $x$, then the second is $x + 1$

The sum is 113, so write an equation to show this..

$x + x + 1 = 113$

$2 x = 113 - 1 \text{ } \leftarrow$ subtract 1 from both sides

$2 x = 112$

$x = 56$