Question

If the sum of two numbers is 12 and their difference is 8, then the product of the two numbers is:

• A. 16
• B. 18
• C. 20
• D. 22

Hint:

When solving for two numbers with their sum and difference, add the equations to find one variable and substitute it back to find the other.

Answer 1

The Correct Option is C

Step 1: Let the two numbers be \( x \) and \( y \). We are given two conditions: \[ x + y = 12 \quad \text{(1)} \quad \text{and} \quad x - y = 8 \quad \text{(2)}. \] Step 2: Add equations (1) and (2) to eliminate \( y \): \[ (x + y) + (x - y) = 12 + 8 \quad \Rightarrow \quad 2x = 20 \quad \Rightarrow \quad x = 10. \] Step 3: Substitute \( x = 10 \) into equation (1): \[ 10 + y = 12 \quad \Rightarrow \quad y = 2. \] Step 4: Now, the product of the two numbers is: \[ x \times y = 10 \times 2 = 20. \]