# The product of a number and 3 is 5 less than the quotient of a number and 3. What is the number?

Sep 11, 2017

The number $\left(n\right)$ is $- \frac{15}{8}$

#### Explanation:

Let's break this down using mathematical symbols:

The product of a number and $3$:

We know that product means multiplication or times. A number is some unknown value which we can call a variable $n$. So this statement translates to $3 \times n$ or $3 n$

is is an equilvent way to say equal to which can be represent using an $=$ sign.

$5$ less than the quotient of a number and $3$:

$5$ less than means some quantity minus $5$ which we can express as $\text{something} - 5$ for now. We also know that the quotient means division or divide$\left(\div i \mathrm{de}\right)$. A number, as we said before is some unknown quantity (or number) that we can call a variable $n$ that will be divided by $3$. Given this, the statement translates to

$\frac{n}{3} - 5$

Putting the entire statement together we get an equation that we can solve for $n$

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

So to solve for $n$, we can start by multiplying $3$ to both sides

$3 \left(3 n\right) = 3 \left(\frac{n}{3} - 5\right)$

$9 n = \frac{3 n}{3} - 15$

$9 n = n - 15$

Subtract $n$ from both sides

$9 n - n = \cancel{n - n} - 15$

$8 n = - 15$

Divide $8$ from both sides to solve for $n$

$\frac{\cancel{8}}{\cancel{8}} n = - \frac{15}{8}$

$n = - \frac{15}{8}$