The average of 2 numbers is M if one number & N, then the other number is _____

Options

A. 2M - N
B. 2 M + N
C. 2M
D. `(M + N)/(2)`

Answer

To find the other number when the average of two numbers is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Average Formula**:
The average of two numbers is given by the formula:
\[ \text{Average} = \frac{\text{Sum of the two numbers}}{\text{Number of observations}} \]

2. **Set Up the Equation**:
We know the average of the two numbers is \( M \). Let’s denote the two numbers as \( n \) (the known number) and \( x \) (the unknown number). Therefore, we can write:
\[ M = \frac{n + x}{2} \]

3. **Multiply Both Sides by 2**:
To eliminate the fraction, multiply both sides of the equation by 2:
\[ 2M = n + x \]

4. **Rearrange the Equation**:
To find \( x \), we need to isolate it on one side of the equation. We can rearrange the equation as follows:
\[ x = 2M - n \]

5. **Conclusion**:
Thus, the other number \( x \) is given by:
\[ x = 2M - n \]

### Final Answer:
The other number is \( 2M - n \).

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