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

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

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Answer 1 · 2016-06-22T17:25:23

$4, 5, 6$ $4,5,6$

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 $n$ $n$ . The second integer, since it is right after the first, will be $n + 1$ $n+1$ . The third integer, since it is right after the second, will be $(n + 1) + 1 = n + 2$ $(n+1)+1=n+2$ .

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

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

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

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

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

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