The sum of three consecutive odd integers is -51, how do you find the numbers?

What I like to do with these problems is take the number and divide by the number of values we're looking fr, int his case, #3#

so #-51/3 = -17#

Now we find two values that are equally distant from #-17#. They need to be odd numbers and consecutive. The two that follow that pattern are #-19# and #-15#

Let's see if this works:

#-19 + -17 + -15 = -51#

We were right!

First, let's call the smallest number: #n#

Then, the next two consecutive odd numbers would be:

#n + 2# and #n + 4#

We know the sum of these is #-51# so we can write this equation and solve for #n#:

#n + (n + 2) + (n + 4) = -51#

#n + n + 2 + n + 4 = -51#

#n + n + n + 2 + 4 = -51#

#1n + 1n + 1n + 2 + 4 = -51#

#(1 + 1 + 1)n + (2 + 4) = -51#

#3n + 6 = -51#

#3n + 6 - color(red)(6) = -51 - color(red)(6)#

#3n + 0 = -57#

#3n = -57#

#(3n)/color(red)(3) = -57/color(red)(3)#

#(color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3)) = -19#

#n = -19#

Therefore:

• #n + 2 = -19 + 2 = -17#

• #n + 4 = -19 + 4 = -15#

The three consecutive odd integers would be: -19, -17 and -15

#-19 + -17 + -15 => -19 - 17 - 15 => -36 - 15 => -51#