# Three consecutive integers have a sum of 78. How do you find the integers?

Nov 5, 2016

$25$, $26$ and $27$ are the three consecutive integers.

#### Explanation:

Let the numbers be represented as $x$, $x + 1$ and $x + 2$.

We can write the equation:

$x + \left(x + 1\right) + \left(x + 2\right) = 78$

Opening the brackets and simplifying:

$x + x + 1 + x + 2 = 78$

$3 x + 3 = 78$

Subtract $3$ from both sides.

$3 x = 75$

Divide both sides by $3$.

$x = 25$

Since the three consecutive integers are $x$, $x + 1$ and $x + 2$, replace $x$ with $25$.

$\therefore 25$, $26$ and $27$ are the three consecutive integers.