A number is divided by 3. Then, 5 is added to the quotient, and the result is 8. What is the number?

Nov 15, 2016

$n = 9$

Explanation:

First, let's give a name to the number we are looking for and call it $n$.

So we can then write "A number is divided by 3" as $\frac{n}{3}$

To add $5$ to the quotient would then give us the expression $\frac{n}{3} + 5$

If this results in $8$ we can finally write the equation we are trying to solve and solve the equation for $n$ while keeping the equation balanced:

$\frac{n}{3} + 5 = 8$

$\frac{n}{3} + 5 - 5 = 8 - 5$

$\frac{n}{3} + 0 = 3$

$\frac{n}{3} = 3$

$3 \cdot \frac{n}{3} = 3 \cdot 3$

$1 n = 9$

$n = 9$