# Two numbers total 36 and have a difference of 12. How do you find the two number?

Dec 6, 2016

The two numbers which solve this problem are $12$ and $24$

#### Explanation:

We can write two different equations from the information provided and then use substitution to solve for the two numbers.

First, lets call the numbers we are looking for $m$ and $n$.

We now can write:

$m + n = 36$ and $m - n = 12$

First, solve the first equation for $m$:

$m + n - n = 36 - n$

$m + 0 = 36 - n$

$m = 36 - n$

Next, we substitute $36 - n$ into the second equation for $m$ and solve for $n$:

$36 - n - n = 12$

$36 - 2 n = 12$

$36 - 2 n + 2 n - 12 = 12 + 2 n - 12$

$36 - 0 - 12 = 0 + 2 n$

$24 = 2 n$

$\frac{24}{2} = \frac{2 n}{2}$

$12 = \frac{\cancel{2} n}{\cancel{2}}$

$12 = n$

Finally, we can substitute $12$ for $n$ in the solution to the first equation and calculate $m$:

$m = 36 - 12$

$m = 24$