The problem asks us to find two numbers based on the following conditions:

1. The larger of the two numbers is 12 more than the smaller number.
2. The sum of the two numbers is 74.

Let’s solve this step-by-step:

1. Define variables:

   • Let $x$ be the smaller number.
   • The larger number is $x + 12$, as given in the problem.

2. Set up an equation based on the sum of the two numbers: $x + (x + 12) = 74$

3. Solve the equation: $2x + 12 = 74$ Subtract 12 from both sides: $2x = 62$ Divide by 2: $x = 31$ So, the smaller number is 31.

4. Find the larger number: The larger number is $x + 12 = 31 + 12 = 43$.

Final answer:

The two numbers are 31 and 43.

Would you like further explanation on any part of this solution, or a more detailed breakdown?

Here are five related questions:

1. What would the sum be if the larger number were 15 more than the smaller one instead?
2. Can you express the relationship between the two numbers as a system of equations?
3. How would the solution change if the sum of the two numbers was 100 instead of 74?
4. What happens if the smaller number is subtracted from the larger number?
5. How can you verify the solution to this problem?

Tip: When solving word problems, clearly defining your variables at the start helps prevent confusion.