The sum of the real numbers x and y is 17. Their difference is 3. What is the value of xy ?

Options

A. `-140`
B. `-60`
C. 11
D. 70

Answer

To solve the problem step by step, we start with the given equations based on the information provided:

1. **Write down the equations**:
- The sum of x and y is given as:
\[ x + y = 17 \quad \text{(Equation 1)} \]
- The difference of x and y is given as:
\[ x - y = 3 \quad \text{(Equation 2)} \]

2. **Add the two equations**:
We can add Equation 1 and Equation 2 to eliminate y:
\[ (x + y) + (x - y) = 17 + 3 \]
Simplifying this gives:
\[ 2x = 20 \]

3. **Solve for x**:
Now, divide both sides by 2 to find the value of x:
\[ x = \frac{20}{2} = 10 \]

4. **Substitute x back into Equation 1**:
Now that we have the value of x, we can substitute it back into Equation 1 to find y:
\[ 10 + y = 17 \]
Rearranging gives:
\[ y = 17 - 10 = 7 \]

5. **Calculate the product xy**:
Now that we have both x and y, we can find the product:
\[ xy = 10 \times 7 = 70 \]

Thus, the value of \( xy \) is **70**.