If the average of the list `{5, 6, 6, 8, 9, x, y}` is 6, then what is the value of `x + y` ?

Answer

To solve the problem, we need to find the value of \( x + y \) given that the average of the list \( \{5, 6, 6, 8, 9, x, y\} \) is 6.

### Step-by-Step Solution:

1. **Understanding the Average**:
The average of a set of numbers is calculated by dividing the sum of all the numbers by the count of the numbers. The formula for average is:
\[ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Number of items}} \]

2. **Setting Up the Equation**:
We know the average is 6 and the list has 7 items (5, 6, 6, 8, 9, x, y). Thus, we can set up the equation:
\[ 6 = \frac{5 + 6 + 6 + 8 + 9 + x + y}{7} \]

3. **Calculating the Sum of Known Numbers**:
First, we calculate the sum of the known numbers:
\[ 5 + 6 + 6 + 8 + 9 = 34 \]
Therefore, we can rewrite our equation as:
\[ 6 = \frac{34 + x + y}{7} \]

4. **Cross-Multiplying**:
To eliminate the fraction, we cross-multiply:
\[ 6 \times 7 = 34 + x + y \]
This simplifies to:
\[ 42 = 34 + x + y \]

5. **Isolating \( x + y \)**:
Now, we isolate \( x + y \) by subtracting 34 from both sides:
\[ x + y = 42 - 34 \]
Simplifying this gives:
\[ x + y = 8 \]

### Final Answer:
Thus, the value of \( x + y \) is \( \boxed{8} \).