Question

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

Answer 1

Step 1: Write the statement into mathematical symbols.

Let the number be a variable say $n$.

The product of a number and $3$ is $n\times 3$.

$5$ less than the quotient of a number and $3$ is $\frac{n}{3}-5$

Put the entire statement together we get an equation for the $n$ variable.

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

Step 2: Solve for n

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

$\Rightarrow 3\left(3n\right)=3(\frac{n}{3}-5)$ (Multiplying both sides by $3$)

$\Rightarrow 9n=n-15$

$\Rightarrow 8n=-15$ (Subtract both sides by $n$)

$\Rightarrow n=-\frac{15}{8}$ (Divide both sides by $8$)

Therefore, the number ($n$) is $-\frac{15}{8}$.