# The sum of two numbers is 17 and their difference is 29. What are the two numbers?

Jul 17, 2017

See a solution process below:

#### Explanation:

First, let's give the two numbers a name:

Number 1: we will call: $n$

Number 2: we will call: $m$

From the information in the problem we can write these two equations:

Equation 1: $n + m = 17$

Equation 2: $n - m = 29$

Step 1 Solve the first equation for $n$:

$n + m = 17$

$n + m - \textcolor{red}{m} = 17 - \textcolor{red}{m}$

$n + 0 = 17 - m$

$n = 17 - m$

Step 2 Substitute $\left(17 - m\right)$ for $n$ in the second equation and solve for $m$:

$n - m = 29$ becomes:

$\left(17 - m\right) - m = 29$

$17 - 1 m - 1 m = 29$

$17 + \left(- 1 - 1\right) m = 29$

$17 + \left(- 2\right) m = 29$

$17 - 2 m = 29$

$- \textcolor{red}{17} + 17 - 2 m = - \textcolor{red}{17} + 29$

$0 - 2 m = 12$

$- 2 m = 12$

$\frac{- 2 m}{\textcolor{red}{- 2}} = \frac{12}{\textcolor{red}{- 2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} m}{\cancel{\textcolor{red}{- 2}}} = - 6$

$m = - 6$

Step 3 Substitute $- 6$ for $m$ in the solution to the first equation at the end of Step 1 and calculate $n$:

$n = 17 - m$ becomes:

$n = 17 - \left(- 6\right)$

$n = 17 + 6$

$n = 23$

The Two Numbers Are: $23$ and $- 6$