Question

If m = 5n and n = p/3, then m =

• A. 3p/5
• B. 5p/3
• C. 3p
• D. 8p/3
• E. 8p

Hint:

These types of substitution problems are fundamental in algebra. Always identify the linking variable (here, \(n\)) and replace it in the target equation to connect the other two variables.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
We need to find an expression for \(m\) in terms of \(p\) by substituting the value of the intermediate variable \(n\).
Step 2: Key Formula or Approach:
We are given:
Equation (1): \(m = 5n\)
Equation (2): \(n = p/3\)
The goal is to substitute the expression for \(n\) from Equation (2) into Equation (1).
Step 3: Detailed Explanation:
Take the first equation:
\[ m = 5n \]
Substitute \(n = p/3\) into this equation:
\[ m = 5 \times \left(\frac{p}{3}\right) \]
Perform the multiplication:
\[ m = \frac{5p}{3} \]
Step 4: Final Answer:
The expression for \(m\) in terms of \(p\) is \(\frac{5p}{3}\), which corresponds to option (B).