# The 3rd number is the sum of the first and the second number. The first number is one more than the third number. How do you find the 3 numbers?

Oct 17, 2015

These conditions are insufficient to determine a single solution.

$a = \text{whatever you like}$
$b = - 1$
$c = a - 1$

#### Explanation:

Let's call the three numbers $a$, $b$ and $c$.

We are given:

$c = a + b$

$a = c + 1$

Using the first equation, we can substitute $a + b$ for $c$ in the second equation as follows:

$a = c + 1 = \left(a + b\right) + 1 = a + b + 1$

Then subtract $a$ from both ends to get:

$0 = b + 1$

Subtract $1$ from both ends to get:

$- 1 = b$

That is: $b = - 1$

The first equation now becomes:

$c = a + \left(- 1\right) = a - 1$

Add $1$ to both sides to get:

$c + 1 = a$

This is essentially the same as the second equation.

There are not enough constraints to determine $a$ and $c$ uniquely.

You can choose any value you like for $a$ and let $c = a - 1$.