What is the value of x if the mean of 21, 26, 49 and x is 32?

Options

A. 30
B. 36
C. 32
D. 34

Answer

To find the value of \( x \) given that the mean of the numbers 21, 26, 49, and \( x \) is 32, we can follow these steps:

### Step 1: Understand the formula for mean
The mean (average) of a set of numbers is calculated by dividing the sum of the numbers by the count of the numbers.

### Step 2: Set up the equation for the mean
We know that the mean of the numbers 21, 26, 49, and \( x \) is 32. Therefore, we can set up the equation:

\[ \text{Mean} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} \]

In this case, the equation becomes:

\[ 32 = \frac{21 + 26 + 49 + x}{4} \]

### Step 3: Multiply both sides by 4
To eliminate the fraction, multiply both sides of the equation by 4:

\[ 32 \times 4 = 21 + 26 + 49 + x \]

Calculating the left side:

\[ 128 = 21 + 26 + 49 + x \]

### Step 4: Calculate the sum of the known numbers
Now, add the numbers 21, 26, and 49:

\[ 21 + 26 = 47 \]
\[ 47 + 49 = 96 \]

So, we have:

\[ 128 = 96 + x \]

### Step 5: Solve for \( x \)
To find \( x \), subtract 96 from both sides:

\[ x = 128 - 96 \]
\[ x = 32 \]

### Conclusion
The value of \( x \) is 32.

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