If the mean of the number 6,y,7,x and 14 is 8. Express y in terms of x.

Answer

To solve the problem step by step, we will find the value of \( y \) in terms of \( x \) given that the mean of the numbers \( 6, y, 7, x, \) and \( 14 \) is \( 8 \).

### Step-by-Step Solution:

1. **Understand the Mean Formula**:
The mean (average) of a set of numbers is calculated by dividing the sum of the numbers by the total count of the numbers.

2. **Set Up the Equation for Mean**:
We know the mean of the numbers \( 6, y, 7, x, \) and \( 14 \) is \( 8 \). Therefore, we can write the equation:
\[ \text{Mean} = \frac{6 + y + 7 + x + 14}{5} = 8 \]

3. **Calculate the Sum**:
First, we need to simplify the sum in the numerator:
\[ 6 + 7 + 14 = 27 \]
So, we can rewrite the equation as:
\[ \frac{27 + y + x}{5} = 8 \]

4. **Multiply Both Sides by 5**:
To eliminate the fraction, multiply both sides of the equation by \( 5 \):
\[ 27 + y + x = 40 \]

5. **Isolate \( y + x \)**:
Now, we will isolate \( y + x \) by subtracting \( 27 \) from both sides:
\[ y + x = 40 - 27 \]
Simplifying this gives:
\[ y + x = 13 \]

6. **Express \( y \) in Terms of \( x \)**:
To express \( y \) in terms of \( x \), we can rearrange the equation:
\[ y = 13 - x \]

### Final Answer:
Thus, \( y \) can be expressed in terms of \( x \) as:
\[ y = 13 - x \]