The sum of three consecutive odd integers is -87. What are the integers?

2 Answers
May 15, 2016

#{-31, -29, -27}#

Explanation:

Any odd integer may be expressed as #2n+1# for some integer #n#. As we are looking for three consecutive odd integers, we will represent the least as #2n+1#, and the next two as #2n+3#, and #2n+5#. With that, we have

#(2n+1)+(2n+3)+(2n+5) = -87#

#=> 6n+9 = -87#

#=> 6n = -96#

#=> n = -16#

Then, the three odd integers are

#{2(-16)+1, 2(-16)+3, 2(-16)+5}#

#= {-31, -29, -27}#

May 15, 2016

#-31, -29, -27#

Explanation:

Alternatively, suppose the second consecutive odd integer is #n#.

Then the first and third are #(n-2)# and #(n+2)#.

So:

#-87 = (n-2)+n+(n+2) = 3n#

Divide both ends by #3# to get:

#-29 = n#

So the three consecutive odd integers are:

#-31, -29, -27#