The sum of three consecutive integers is 15. What are the integers?

Jun 22, 2016

$4 , 5 , 6$

Explanation:

When solving algebraic problems, the first thing we have to do is define a variable for stuff that we don't know. In this problem, we don't know any of the integers, so we assign a variable to them.

Let's have the first integer be $n$. The second integer, since it is right after the first, will be $n + 1$. The third integer, since it is right after the second, will be $\left(n + 1\right) + 1 = n + 2$.

The illustrate this concept, consider the integers $1$, $2$, and $3$. $2$ is one more than $1$, or in other words, $2 = 1 + 1$. Ditto for $3$, except $3$ is two more than $1$, so $3 = 1 + 2$. Since the integers are consecutive, each is one more than the last.

We're told that the sum of our three integers is $15$. Therefore,
$n + \left(n + 1\right) + \left(n + 2\right) = 15$

Solving this equation is pretty straightforward:
$3 n + 3 = 15$
$3 n = 12$
$n = 4$

That means our first integer is $4$. Our second integer is $4 + 1$, or $5$, and our third integer is $5 + 1$, or $6$. Our answer is confirmed because $4 + 5 + 6 = 15$.