If the mean of 10,14,7,9 and x is x, then find the value of x ?

Options

A. 4
B. 5
C. 8
D. 10

Answer

To solve the problem step by step, we need to find the value of \( x \) given that the mean of the numbers 10, 14, 7, 9, and \( x \) is equal to \( x \).

### Step 1: Write down the formula for the mean.
The mean (average) of a set of numbers is calculated using the formula:

\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Total number of observations}} \]

### Step 2: Identify the observations and their sum.
The observations given are 10, 14, 7, 9, and \( x \). First, we need to find the sum of these observations:

\[ \text{Sum} = 10 + 14 + 7 + 9 + x \]

Calculating the sum of the constant numbers:

\[ 10 + 14 = 24 \]
\[ 24 + 7 = 31 \]
\[ 31 + 9 = 40 \]

So, the sum of the observations is:

\[ \text{Sum} = 40 + x \]

### Step 3: Determine the total number of observations.
The total number of observations is 5 (the numbers 10, 14, 7, 9, and \( x \)).

### Step 4: Set up the equation for the mean.
According to the problem, the mean is equal to \( x \):

\[ \frac{40 + x}{5} = x \]

### Step 5: Multiply both sides by 5 to eliminate the fraction.
To eliminate the fraction, multiply both sides by 5:

\[ 40 + x = 5x \]

### Step 6: Rearrange the equation to isolate \( x \).
Now, we want to get all terms involving \( x \) on one side:

\[ 40 = 5x - x \]
\[ 40 = 4x \]

### Step 7: Solve for \( x \).
Now, divide both sides by 4 to find the value of \( x \):

\[ x = \frac{40}{4} = 10 \]

### Conclusion:
The value of \( x \) is 10.

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