The sum of two numbers is 12 and the difference of their squares is 60. The difference between the numbers is

(A) 3

(B) 5

(C) 7

(D) 9

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.

The sum of two numbers is 12 and the difference of their squares is 60. The difference between the numbers is (A) 3 (B) 5 (C) 7 (D) 9

Learn how to find the difference between two numbers when their sum is 12 and the difference of their squares is 60. This solution uses the difference of squares formula and linear equations, suitable for students in Grades 8-10.

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