The sum of two numbers is 16 and their difference is 2. What is the product of the two numbers?

Options

A. 35
B. 56
C. 63
D. 72

Answer

To solve the problem, we need to find two numbers based on the given conditions: their sum is 16, and their difference is 2. We will denote these two numbers as \( a \) and \( b \).

### Step-by-Step Solution:

1. **Set Up the Equations**:
- From the problem, we have two equations:
\[ a + b = 16 \quad \text{(1)} \]
\[ a - b = 2 \quad \text{(2)} \]

2. **Add the Two Equations**:
- To eliminate \( b \), we can add equations (1) and (2):
\[ (a + b) + (a - b) = 16 + 2 \]
- This simplifies to:
\[ 2a = 18 \]

3. **Solve for \( a \)**:
- Divide both sides by 2:
\[ a = \frac{18}{2} = 9 \]

4. **Substitute \( a \) Back into Equation (1)**:
- Now that we have \( a \), we can find \( b \) by substituting \( a \) back into equation (1):
\[ 9 + b = 16 \]
- Rearranging gives:
\[ b = 16 - 9 = 7 \]

5. **Calculate the Product**:
- Now that we have both numbers \( a = 9 \) and \( b = 7 \), we can find their product:
\[ a \times b = 9 \times 7 = 63 \]

### Final Answer:
The product of the two numbers is \( 63 \).