# Question #b5a9e

Nov 30, 2016

10 and 22 total 32 but have a difference of 12.

#### Explanation:

First, let's call our two numbers $x$ and $y$.

We know from the problem:

$x + y = 32$

We also know:

$x - y = 12$

Next, solve the first equation for $x$:

$x + y - y = 32 - y$

$x + 0 = 32 - y$

$x = 32 - y$

Now we can substitute $32 - y$ for $x$ in the second equation and determine the value of $y$:

$\left(32 - y\right) - y = 12$

$32 - 2 y = 12$

$32 - 32 - 2 y = 12 - 32$

$0 - 2 y = - 2$

$- 2 y = - 20$

$\frac{- 2 y}{-} 2 = \frac{- 20}{- 2}$

$y = 10$

We can now substitute $10$ for $y$ in the solution for the first equation and calculate $x$:

$x = 32 - 10$

$x = 22$