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

Mar 14, 2018

$- 19 , - 17 , - 15$

#### Explanation:

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 $- \frac{51}{3} = - 17$

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!

Mar 14, 2018

See a solution process below:

#### Explanation:

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 $n$:

$n + \left(n + 2\right) + \left(n + 4\right) = - 51$

$n + n + 2 + n + 4 = - 51$

$n + n + n + 2 + 4 = - 51$

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

$\left(1 + 1 + 1\right) n + \left(2 + 4\right) = - 51$

$3 n + 6 = - 51$

$3 n + 6 - \textcolor{red}{6} = - 51 - \textcolor{red}{6}$

$3 n + 0 = - 57$

$3 n = - 57$

$\frac{3 n}{\textcolor{red}{3}} = - \frac{57}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} n}{\cancel{\textcolor{red}{3}}} = - 19$

$n = - 19$

Therefore:

• $n + 2 = - 19 + 2 = - 17$

• $n + 4 = - 19 + 4 = - 15$

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

$- 19 + - 17 + - 15 \implies - 19 - 17 - 15 \implies - 36 - 15 \implies - 51$