To solve the equation \( s = \frac{p}{3} (b + k) \) for \( k \), follow these steps:

1. **Isolate the term involving \( k \)**:  
   Multiply both sides of the equation by 3 to eliminate the fraction:
   \[
   3s = p(b + k)
   \]

2. **Divide by \( p \)** to further isolate \( k \)**:  
   \[
   \frac{3s}{p} = b + k
   \]

3. **Solve for \( k \)**:  
   Subtract \( b \) from both sides:
   \[
   k = \frac{3s}{p} - b
   \]

So, the solution for \( k \) is:
\[
k = \frac{3s}{p} - b
\]

Would you like more details on this solution or have any other questions?

Here are five related questions to consider:
1. How would you solve the equation if you needed to solve for \( b \) instead of \( k \)?
2. What changes if the equation is \( s = \frac{p}{2} (b + k) \) instead?
3. How can this equation be used in a real-world context, such as calculating a final value \( k \) based on given values?
4. What are the implications of the value of \( p \) on the solution for \( k \)?
5. How would you solve the equation if the term \( p \) was replaced with another expression, like \( p + q \)?

**Tip:** When dealing with equations involving fractions, multiplying both sides by the denominator is a useful first step to simplify the equation.

Learn how to solve the equation s = p/3 (b + k) step-by-step. Understand the manipulation of fractions and algebraic terms to isolate k. Suitable for students and professionals dealing with algebraic equations and fractional manipulations.

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