# The larger of two numbers is 1 less than 8 times the smaller. Their sum is 179. How do you find the numbers?

Oct 2, 2015

The two numbers are $20$ and $159$

#### Explanation:

Define
$\textcolor{w h i t e}{\text{XXX}} b =$bigger (larger) number
$\textcolor{w h i t e}{\text{XXX}} s =$smaller number

We are told
[1]$\textcolor{w h i t e}{\text{XXX}} b = 8 s - 1$
[2]$\textcolor{w h i t e}{\text{XXX}} b + s = 179$

Substituting $\left(8 s - 1\right)$ for $b$ (from [1]) into [2]
[3]$\textcolor{w h i t e}{\text{XXX}} 8 s - 1 + s = 179$

Simplify
[4]$\textcolor{w h i t e}{\text{XXX}} 9 s = 180$

[5]$\textcolor{w h i t e}{\text{XXX}} s = 20$

Substituting $20$ for $s$ in [2]
[6]$\textcolor{w h i t e}{\text{XXX}} b + 20 = 179$

[7]$\textcolor{w h i t e}{\text{XXX}} b = 159$