# The sum of three consecutive numbers is 42. What is the smallest of these numbers?

Dec 16, 2016

The smallest of the three consecutive integers summing to 42 is 13.

#### Explanation:

Let's call the smallest of the three consecutive numbers $s$.

The next two consecutive integers, by definition of consecutive and the fact they are integers as: $s + 1$ and $s + 2$

We know there sum is 42 so we can add our three numbers and solve for $s$:

$s + \left(s + 1\right) + \left(s + 2\right) = 42$

$s + s + 1 + s + 2 = 42$

$3 s + 3 = 42$

$3 s + 3 - 3 = 42 - 3$

$3 s + 0 = 39$

$3 s = 39$

$\frac{3 s}{3} = \frac{39}{3}$

$s = 13$

Checking the solution:

The three consecutive integers would be:

$13$

$13 + 1 = 14$

$13 + 2 = 15$

Adding the three integers gives:

$13 + 14 + 15 = 27 + 15 = 42$