This is a common factor puzzle. The goal is to find two numbers that:

1. Multiply to give the value on top (30).
2. Add to give the value on the bottom (11).

We need to find two numbers that satisfy these conditions:

• Their product is 30.
• Their sum is 11.

Step-by-Step Solution:

1. Let's list the factor pairs of 30:

   • (1, 30)
   • (2, 15)
   • (3, 10)
   • (5, 6)

2. Now, we check which of these pairs adds up to 11:

   • 1 + 30 = 31 (No)
   • 2 + 15 = 17 (No)
   • 3 + 10 = 13 (No)
   • 5 + 6 = 11 (Yes)

Thus, the two numbers are 5 and 6.

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

Related Questions:

1. How do you factor quadratic equations using these types of puzzles?
2. Can you solve similar puzzles with negative numbers?
3. How can you generalize this method for larger numbers?
4. How is this approach used in solving polynomial equations?
5. Can you apply this method to solve systems of equations?

Tip:

Always check both the product and the sum conditions when solving these types of factor puzzles!