The quotient of p and q is twelve less thanthree times the sum of p and q .Which of the following equations represents thestatement above?

To find the equation that represents the given statement, we first need to break it down into its components.

1. ### Break Down the Problem

1. The quotient of $p$ and $q$ can be expressed as $\frac{p}{q}$.
2. The phrase "twelve less than three times the sum of $p$ and $q$" can be broken down into:
   • The sum of $p$ and $q$ is $p + q$.
   • Three times this sum is $3(p + q)$.
   • Twelve less than this is $3(p + q) - 12$.

2. ### Relevant Concepts

Now we can set up the equation based on the statement: $\frac{p}{q} = 3(p + q) - 12$

3. ### Analysis and Detail

This equation directly relates $\frac{p}{q}$ with the expression $3(p + q) - 12$, as requested in the problem statement.

4. ### Verify and Summarize

This equation captures the relationship described in the problem accurately. One can expand $3(p + q)$ to verify that it reveals the correct transformation.

Final Answer

The equation that represents the statement is: $\frac{p}{q} = 3(p + q) - 12$