if pp and qq vary inversely and pp is 10 when qq is 16, determine qq when pp is equal to 5.

If \( pp \) and \( qq \) vary inversely, this means that their product is constant. Mathematically, this relationship can be expressed as:

\[
pp \times qq = k
\]

where \( k \) is a constant. 

Given that \( pp = 10 \) when \( qq = 16 \), we can first find the value of \( k \):

\[
10 \times 16 = 160
\]

So, \( k = 160 \).

Now, we are asked to determine \( qq \) when \( pp = 5 \). Using the same inverse variation equation:

\[
5 \times qq = 160
\]

Solving for \( qq \):

\[
qq = \frac{160}{5} = 32
\]

Thus, when \( pp = 5 \), \( qq = 32 \).

Would you like more details on inverse variation or how I derived this? 

Here are 5 related questions to expand your understanding:
1. How does the concept of inverse variation apply to real-world problems?
2. What happens to \( qq \) if \( pp \) is doubled in an inverse relationship?
3. Can you explain how inverse variation differs from direct variation?
4. How do you solve for \( pp \) given \( qq \) and the constant \( k \)?
5. What would the graph of an inverse variation relationship look like?

**Tip**: When dealing with inverse variation, remember that as one quantity increases, the other decreases proportionally.

If pp and qq vary inversely and pp is 10 when qq is 16, determine qq when pp is equal to 5.

Solve the inverse variation problem where pp = 10 when qq = 16. Learn how to determine qq when pp = 5 using the inverse variation formula. This algebraic problem is ideal for students in Grades 7-9, demonstrating key concepts in inverse relationships.

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