The 4 integers j,j,k and n have an average of 0. which of the following equations must be true ?

Options

A. `k=n`
B. `k=-j`
C. `k+n=-2j`
D. `k+n=0`

Answer

To solve the problem, we need to find the relationship between the integers \( j, j, k, \) and \( n \) given that their average is 0.

### Step-by-Step Solution:

1. **Understanding the Average**:
The average of the integers \( j, j, k, \) and \( n \) is given by the formula:
\[ \text{Average} = \frac{\text{Sum of values}}{\text{Number of values}} \]
Here, the sum of the values is \( j + j + k + n \) and the number of values is 4.

2. **Setting Up the Equation**:
Since the average is given to be 0, we can set up the equation:
\[ \frac{j + j + k + n}{4} = 0 \]

3. **Simplifying the Equation**:
Multiply both sides of the equation by 4 to eliminate the denominator:
\[ j + j + k + n = 0 \]
This simplifies to:
\[ 2j + k + n = 0 \]

4. **Rearranging the Equation**:
To find a relationship among \( j, k, \) and \( n \), we can rearrange the equation:
\[ k + n = -2j \]

5. **Conclusion**:
The equation \( k + n = -2j \) must be true given that the average of \( j, j, k, \) and \( n \) is 0.

### Final Answer:
The equation that must be true is:
\[ k + n = -2j \]