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The problem from the image states:

"Given that \( x \) is 30% greater than \( p \) and \( y \) is 60% greater than \( q \), how many percent is \( xy \) greater than \( pq \)?"

### Step-by-Step Solution:

1. **Express \( x \) and \( y \) in terms of \( p \) and \( q \):**

   - Since \( x \) is 30% greater than \( p \), we can write:
     \[
     x = p \times (1 + 0.30) = 1.3p
     \]
   
   - Since \( y \) is 60% greater than \( q \), we can write:
     \[
     y = q \times (1 + 0.60) = 1.6q
     \]

2. **Find the product \( xy \):**
   \[
   xy = (1.3p) \times (1.6q) = 2.08pq
   \]

3. **Determine the percentage increase from \( pq \) to \( xy \):**

   To find how much greater \( xy \) is than \( pq \), we compare them:
   \[
   \text{Increase} = xy - pq = 2.08pq - pq = 1.08pq
   \]
   
   So, the increase is \( 1.08pq \), which is 108% of \( pq \).

   Therefore, \( xy \) is **108% greater** than \( pq \).

Would you like further details or have any other questions?

Here are 5 related questions to extend your understanding:
1. How do you calculate the percentage increase of a product of two variables?
2. How would the result change if \( x \) were 50% greater than \( p \) instead of 30%?
3. Can this method be generalized for other percentage increases in \( x \) and \( y \)?
4. What if \( x \) were 30% less than \( p \)? How would that affect the result?
5. How does this concept apply to real-world situations involving percentage increases?

**Tip**: When solving percentage problems involving products, express the percentage as a decimal multiplier to simplify calculations.

Given that x is 30% greater than p and y is 60% greater than q, how many percent is xy greater than pq?

Learn how to calculate how much greater xy is compared to pq, where x is 30% greater than p, and y is 60% greater than q. This problem involves percentage increases and multiplication of expressions, suitable for Grades 8-10.

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