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 1: Understand the concept of average
The average of a set of numbers is calculated by dividing the sum of the numbers by the total count of the numbers.

### Step 2: Set up the equation for the average
Given that the average of four numbers is 10.5, we can express this mathematically as:
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Total count of numbers}} \]
For our case:
\[ 10.5 = \frac{4 + 9 + 13 + x}{4} \]
where \(x\) is the fourth number we need to find.

### Step 3: Calculate the sum of the known numbers
First, we need to calculate the sum of the three known numbers:
\[ 4 + 9 + 13 = 26 \]

### Step 4: Substitute the sum into the average equation
Now we can substitute the sum of the known numbers into the average equation:
\[ 10.5 = \frac{26 + x}{4} \]

### Step 5: Multiply both sides by 4 to eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by 4:
\[ 10.5 \times 4 = 26 + x \]
Calculating the left side:
\[ 42 = 26 + x \]

### Step 6: Solve for the fourth number
Now, we can solve for \(x\) by isolating it:
\[ x = 42 - 26 \]
Calculating the right side:
\[ x = 16 \]

### Conclusion
The fourth number is \(16\).

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