# The sum of 3 consecutive odd integers is 57, what is the smallest integer?

Feb 24, 2016

First, we can call the smallest of the odd integers $x$

Then, we find the next odd integer

Well, odd integers come every other number, so let's say we start from 1. We must add 2 more to 1 to get to the consecutive odd integer

So the middle of our consecutive odd integers can be expressed as $x + 2$

We can apply the same method for the last odd integer, it is 4 more than the first odd integer, so it can be seen as $x + 4$

We are finding the sum to be 57, so we create the equation

$x + x + 2 + x + 4 = 57$

Combine like terms: $3 x + 6 = 57$

Subtract: $3 x = 51$

Divide: $x = 17$

So, our integers are $17 , 19 , 21$

Check them really quickly, and they work!

The question asks for the smallest of the integers, which would be 17