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?

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Answer 1 · 2016-12-11T01:07:32

The number is $- 22.5$ $color(green)(-22.5)$

Let the number be $n$ $n$

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

$1/5n-5=n+13$

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

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

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

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

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