Average of four numbers is 10.5. If three of these numbers be 4, 9 and 13, find the fourth number.

Options

A. 16
B. 17
C. Cannot be determined
D. None of the above

Answer

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

### Step-by-Step Solution:

1. **Understand the Average Formula**:
The average of a set of numbers is calculated by dividing the sum of the numbers by the total count of the numbers. In this case, the average of four numbers is given as 10.5.

\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Total count of numbers}} \]

2. **Set Up the Equation**:
Let the fourth number be \( X \). The three known numbers are 4, 9, and 13. Therefore, the sum of the four numbers can be expressed as:

\[ \text{Sum} = 4 + 9 + 13 + X \]

3. **Calculate the Known Sum**:
First, calculate the sum of the known numbers:

\[ 4 + 9 + 13 = 26 \]

So, the equation for the sum becomes:

\[ \text{Sum} = 26 + X \]

4. **Set Up the Average Equation**:
Now, using the average provided (10.5), we can set up the equation:

\[ 10.5 = \frac{26 + X}{4} \]

5. **Multiply Both Sides by 4**:
To eliminate the fraction, multiply both sides of the equation by 4:

\[ 10.5 \times 4 = 26 + X \]

This simplifies to:

\[ 42 = 26 + X \]

6. **Solve for \( X \)**:
Now, isolate \( X \) by subtracting 26 from both sides:

\[ X = 42 - 26 \]

This gives:

\[ X = 16 \]

### Final Answer:
The fourth number is **16**.

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