# The sum of three consecutive integers is 582. What are the integers?

Jul 6, 2016

$\left\{193 , 194 , 195\right\}$

#### Explanation:

Let $n$ be the least of the integers. Then the next two consecutive integers are $n + 1$ and $n + 2$, and we have

$n + \left(n + 1\right) + \left(n + 2\right) = 582$

$\implies 3 n + 3 = 582$

$\implies 3 n = 582 - 3 = 579$

$\implies n = \frac{579}{3} = 193$

Therefore the three consecutive integers are $\left\{193 , 194 , 195\right\}$

Checking our answer, we find that $193 + 194 + 195 = 582$, as desired.

Jul 6, 2016

The reqd. ints. are, 193,194, & 195.

#### Explanation:

We require consecutive integers, so, if we start with $x$, the following/succeeding ints. must be $x + 1$ & $\left(x + 1\right) + 1 = x + 2$.

Then, by what is given, $x + \left(x + 1\right) + \left(x + 2\right) = 582$, i.e., $3 x + 3 = 582$, or, $3 x = 582 - 3 , = 579$, giving, x=579/3,=193; (x+1)=194, &, (x+2)=195.

Observe that they fulfil the given cond.

The reqd. ints. are, 193,194, & 195.