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

1 Answer
Ken C.
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 #(n+1)+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+(n+1)+(n+2)=15#

Solving this equation is pretty straightforward:
#3n+3=15#
#3n=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#.

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