The average of 2 numbers is ab. If one of the numberis a, the other is:

Options

A. `2ab -b`
B. `2a-b`
C. `2ab -a`
D. `2b -a`

Answer

To solve the problem, we need to find the other number when the average of two numbers is given as \( ab \) and one of the numbers is \( a \).

### Step-by-Step Solution:

1. **Understand the Concept of Average**:
The average of two numbers is calculated by taking the sum of the numbers and dividing it by the total number of numbers. In this case, we have two numbers, which we can denote as \( a \) and \( x \).

2. **Set Up the Equation**:
The average of the two numbers is given as \( ab \). Therefore, we can write the equation for the average:
\[ \text{Average} = \frac{a + x}{2} \]
Setting this equal to \( ab \):
\[ \frac{a + x}{2} = ab \]

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

4. **Isolate \( x \)**:
Now, we need to solve for \( x \). We can do this by subtracting \( a \) from both sides:
\[ x = 2ab - a \]

5. **Final Expression**:
Thus, the other number \( x \) can be expressed as:
\[ x = a(2b - 1) \]

### Conclusion:
The other number is \( a(2b - 1) \).