# Aiden wrote a riddle: Five less than 1/5 times a number is the same as the sum of the number and 1/3. How do you find the number?

Dec 11, 2016

The number is $\textcolor{g r e e n}{- 22.5}$

#### Explanation:

Let the number be $n$

{: ("Five less than 1/5 times a number: ",1/5n-5), ("is the same as: ",=), ("the sum of the number and 1/3",n+13) :}

$\frac{1}{5} n - 5 = n + 13$

Multiply both sides by $5$
$n - 25 = 5 n + 65$

Subtract $n$ from both sides
$- 25 = 4 n + 65$

Subtract $65$ from both sides
$- 90 = 4 n$

Divide both sides by $4$
$- 22.5 = n$

Exchange sides (not necessary, but most people like it better this way)
$n = - 22.5$