Average of `"43,57,68,32,97 and x is 63"`. What is the value of x?

Options

A. 83
B. 77
C. 81
D. 75

Answer

To find the value of \( x \) in the problem where the average of the numbers \( 43, 57, 68, 32, 97, \) and \( x \) is \( 63 \), we can follow these steps:

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

### Step 2: Set up the equation
We know that the average is \( 63 \) and the numbers we have are \( 43, 57, 68, 32, 97, \) and \( x \). The number of observations is \( 6 \) (since we have 5 known numbers and one unknown \( x \)). Thus, we can set up the equation:
\[ 63 = \frac{43 + 57 + 68 + 32 + 97 + x}{6} \]

### Step 3: Calculate the sum of known numbers
First, we need to calculate the sum of the known numbers:
\[ 43 + 57 + 68 + 32 + 97 \]
Calculating step-by-step:
- \( 43 + 57 = 100 \)
- \( 100 + 68 = 168 \)
- \( 168 + 32 = 200 \)
- \( 200 + 97 = 297 \)

So, the sum of the known numbers is \( 297 \).

### Step 4: Substitute the sum back into the equation
Now we can substitute this back into our average equation:
\[ 63 = \frac{297 + x}{6} \]

### Step 5: Multiply both sides by 6 to eliminate the fraction
To eliminate the fraction, multiply both sides by \( 6 \):
\[ 63 \times 6 = 297 + x \]
Calculating \( 63 \times 6 \):
\[ 378 = 297 + x \]

### Step 6: Solve for \( x \)
Now, we need to isolate \( x \):
\[ x = 378 - 297 \]
Calculating \( 378 - 297 \):
\[ x = 81 \]

### Conclusion
The value of \( x \) is \( 81 \).