Question

If p = 3m and m = k/6, what is the value of p when k = 36?

• A. 2
• B. 6
• C. 12
• D. 18
• E. 108

Hint:

For chained variable problems, substitution can often be faster. Creating a single equation relating the first and last variables (\(p = k/2\)) can simplify the calculation, especially if you need to solve for multiple values of \(k\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This problem involves a chain of dependencies between variables. We are given the value of one variable (\(k\)) and need to work through the given equations to find the value of the final variable (\(p\)).
Step 2: Key Formula or Approach:
1. Use the value of \(k\) to find the value of the intermediate variable \(m\).
2. Use the value of \(m\) to find the final value of \(p\).
Alternatively, first create a direct relationship between \(p\) and \(k\) by substitution.
Step 3: Detailed Explanation:
Method 1: Step-by-step calculation
We are given \(k = 36\).
First, find \(m\) using the equation \(m = k/6\):
\[ m = \frac{36}{6} = 6 \]
Now that we have \(m=6\), we can find \(p\) using the equation \(p = 3m\):
\[ p = 3 \times 6 = 18 \]
Method 2: Substitution first
Substitute the expression for \(m\) into the equation for \(p\):
\[ p = 3m = 3 \left(\frac{k}{6}\right) = \frac{3k}{6} = \frac{k}{2} \]
Now, substitute the value \(k = 36\) into this new equation:
\[ p = \frac{36}{2} = 18 \]
Step 4: Final Answer:
The value of \(p\) is 18, which corresponds to option (D).