To solve this problem, we need to find two numbers that:

1. Multiply to give the top number, 24.
2. Add to give the bottom number, 11.

Let's break it down step-by-step:

1. Find factor pairs of 24:
   The pairs of numbers that multiply to 24 are:

   • $1 \times 24$
   • $2 \times 12$
   • $3 \times 8$
   • $4 \times 6$

2. Check which pair adds up to 11:

   • $1 + 24 = 25$
   • $2 + 12 = 14$
   • $3 + 8 = 11$ ← This pair works.

So, the two numbers are 3 and 8.

Answer:

The two numbers that satisfy these conditions are 3 and 8.

Would you like further details on this solution, or do you have any other questions?

Here are five related questions to expand on this topic:

1. How can we find factor pairs of a number systematically?
2. What other pairs could work if we change the target sum or product?
3. Can we apply this method to solve quadratic equations?
4. How would this approach differ if one of the numbers had to be negative?
5. What are some practical applications of finding two numbers that satisfy both a sum and product condition?

Tip: When searching for pairs, start with smaller factors to make the calculations easier.