How do you find three consecutive integers whose sum is 171?

May 30, 2015

Let the integers be $n - 1$, $n$ and $n + 1$.

Then

$171 = \left(n - 1\right) + n + \left(n + 1\right) = n - 1 + n + n + 1 = 3 n$

Divide both ends by $3$ to get

$n = 57$

So the three consecutive integers are $56$, $57$, $58$.