# How do you find 3 consecutive odd integers where the sum is -141?

May 24, 2018

See a solution process below:

#### Explanation:

Let's call the first odd integer: $n$

Then the next two consecutive odd integers will be:

$n + 2$ and $n + 4$

We can then write this equation and solve for $n$;

$n + \left(n + 2\right) + \left(n + 4\right) = - 141$

$n + n + 2 + n + 4 = - 141$

$n + n + n + 2 + 4 = - 141$

$1 n + 1 n + 1 n + 2 + 4 = - 141$

$\left(1 + 1 + 1\right) n + \left(2 + 4\right) = - 141$

$3 n + 6 = - 141$

$3 n + 6 - \textcolor{red}{6} = - 141 - \textcolor{red}{6}$

$3 n + 0 = - 147$

$3 n = - 147$

$\frac{3 n}{\textcolor{red}{3}} = - \frac{147}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} n}{\cancel{\textcolor{red}{3}}} = - 49$

$n = - 49$

Therefore:

$n + 2 = - 49 + 2 = - 47$

$n + 4 = - 49 + 4 = - 45$

The 3 consecutive odd integers summing to -141 are: -49, -47, -45

Solution Check:

$- 49 - 47 - 45 = - 96 - 45 = - 141$

May 24, 2018

the three numbers are -49,-47 and -45

#### Explanation:

Let the first odd number be $x$
Then, the consecutive odd number is $x + 2$
The last consecutive odd number is $x + 4$

Why do we add 2 to each odd number?
Well, think of any three consecutive odd numbers.

135,137,139
186395,186397,186399

From the above, you can see that when you minus 2 consecutive numbers, you will always get a difference of 2

Since their sum equals to $- 141$,

$x + \left(x + 2\right) + \left(x + 4\right) = - 141$
$3 x + 6 = - 141$
$3 x = - 147$
$x = - 49$

Therefore, your first odd number is -49
Your second number is $- 49 + 2 = - 47$
Your third number is $- 47 + 2 = - 45$

Now, just to make sure you are right, add the numbers together

$- 49 - 47 - 45 = - 141$