$p$ varies inversely as $q$, and $p=18$ when $q=9$. If $q=12$, what is the value of $p$?

• A. $13.5$
• B. $162$
• C. $24$
• D. $12$

Answer: (A)

Verified step by step guidance

1. Understand that since \( p \) varies inversely as \( q \), their relationship can be written as \( p = \frac{k}{q} \), where \( k \) is a constant.
2. Use the given values \( p = 18 \) when \( q = 9 \) to find the constant \( k \). Substitute these values into the equation: \( 18 = \frac{k}{9} \).
3. Solve for \( k \) by multiplying both sides of the equation by 9: \( k = 18 \times 9 \).
4. Now that you have \( k \), use the inverse variation formula \( p = \frac{k}{q} \) again, but this time substitute \( q = 12 \) and the value of \( k \) you found.
5. Calculate \( p \) by dividing \( k \) by 12: \( p = \frac{k}{12} \). This will give you the value of \( p \) when \( q = 12 \).