The average of 23,27,29,36,47 and x is 35. What is the value of x?

Options

A. A) `45`
B. B) `52`
C. C) `48`
D. D) `39`

Answer

To find the value of \( x \) such that the average of the numbers 23, 27, 29, 36, 47, and \( x \) is 35, we can follow these steps:

### Step 1: Write the formula for average
The average of a set of numbers is calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of all values}}{\text{Number of values}} \]

### Step 2: Identify the numbers and the average
In this case, the numbers are 23, 27, 29, 36, 47, and \( x \). The average is given as 35.

### Step 3: Set up the equation
We can set up the equation based on the average:
\[ 35 = \frac{23 + 27 + 29 + 36 + 47 + x}{6} \]

### Step 4: Calculate the sum of the known numbers
First, we need to calculate the sum of the known numbers:
\[ 23 + 27 + 29 + 36 + 47 = 162 \]

### Step 5: Substitute the sum into the equation
Now substitute the sum back into the equation:
\[ 35 = \frac{162 + x}{6} \]

### Step 6: Multiply both sides by 6 to eliminate the fraction
To eliminate the fraction, multiply both sides by 6:
\[ 35 \times 6 = 162 + x \]
\[ 210 = 162 + x \]

### Step 7: Solve for \( x \)
Now, isolate \( x \) by subtracting 162 from both sides:
\[ x = 210 - 162 \]
\[ x = 48 \]

### Final Answer
Thus, the value of \( x \) is \( 48 \).

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