Question

Suppose that $n$ is an integer such that $\frac{n}{3}$ is $12$ greater than $\frac{n}{2}$. Find the value of $n$.

• A. $-72$
• B. $-36$
• C. $-24$
• D. $24$
• E. $72$

Answer 1

The correct option is A $-72$

First, convert the words into an equation:
$\frac{n}{3}=\frac{n}{2}+12$
From here, you could work with the answers by substituting them into the equation, until it works or use algebra to solve the equation:
$\frac{n}{3}-\frac{n}{2}=\frac{2n}{6}-\frac{3n}{6}=-\frac{n}{6}=12$
So that $n=-72$. (You could also solve the equation by multiplying through by 6 first to get rid of the fractions.)