The average of 23, 34, x, 21, 19 and 18 is 21. What is the value of x?

Options

A. 9
B. 10
C. 11
D. 12

Answer

To find the value of \( x \) in the equation where the average of the numbers 23, 34, \( x \), 21, 19, and 18 is 21, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Average Formula**:
The average of a set of numbers is given by the formula:
\[ \text{Average} = \frac{\text{Sum of all values}}{\text{Number of values}} \]

2. **Identify the Values**:
The values we have are 23, 34, \( x \), 21, 19, and 18. The number of values is 6.

3. **Set Up the Equation**:
According to the problem, the average is given as 21. Therefore, we can set up the equation:
\[ 21 = \frac{23 + 34 + x + 21 + 19 + 18}{6} \]

4. **Multiply Both Sides by 6**:
To eliminate the fraction, multiply both sides by 6:
\[ 21 \times 6 = 23 + 34 + x + 21 + 19 + 18 \]
\[ 126 = 23 + 34 + x + 21 + 19 + 18 \]

5. **Calculate the Sum of Known Values**:
Now, calculate the sum of the known values:
\[ 23 + 34 + 21 + 19 + 18 = 115 \]

6. **Substitute Back into the Equation**:
Now substitute this sum back into the equation:
\[ 126 = 115 + x \]

7. **Isolate \( x \)**:
To find \( x \), subtract 115 from both sides:
\[ x = 126 - 115 \]
\[ x = 11 \]

### Final Answer:
The value of \( x \) is \( 11 \).