Let the two numbers be $x$ and $y$.

Given:

• The sum of the two numbers: $x + y = 12$
• The difference of their squares: $x^2 - y^2 = 60$

Step 1: Use the identity for the difference of squares:

$x^2 - y^2 = (x - y)(x + y)$ Substituting the given values: $(x - y)(12) = 60$

Step 2: Solve for $x - y$:

$x - y = \frac{60}{12} = 5$

Thus, the difference between the numbers is $\boxed{5}$.

Would you like more details on any part of this solution?

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Here are 5 related questions:

1. What is the product of the two numbers?
2. How do you find the numbers given $x + y = 12$ and $x - y = 5$?
3. What is the sum of the squares of the two numbers?
4. How would the solution change if the sum was different?
5. Can you solve this problem geometrically?

Tip: The difference of squares formula is a useful tool for simplifying expressions in algebra.