# The sum of two numbers is 48, their difference is 24. What are the numbers?

Feb 13, 2017

The two numbers are 12 and 36

#### Explanation:

First, let's name the two numbers $n$ and $m$.

Then we can write:

$n + m = 48$

and

$n - m = 24$

Step 1) Solve the first equation for $n$:

$n + m = 48$

$n + m - \textcolor{red}{m} = 48 - \textcolor{red}{m}$

$n + 0 = 48 - m$

$n = 48 - m$

Step 2) Substitute $48 - m$ for $n$ in the second equation and solve for $m$:

$n - m = 24$ becomes:

$48 - m - m = 24$

$48 - 2 m = 24$

$- \textcolor{red}{48} + 48 - 2 m = - \textcolor{red}{48} + 24$

$0 - 2 m = - 24$

$- 2 m = - 24$

$\frac{- 2 m}{\textcolor{red}{- 2}} = \frac{- 24}{\textcolor{red}{- 2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} m}{\cancel{\textcolor{red}{- 2}}} = 12$

$m = 12$

Step 3) Substitute $12$ for $m$ in the solution to the first equation at the end of Step 1 and calculate $n$:

$n = 48 - m$ becomes:

$n = 48 - 12$

$n = 36$