If the average of 39, 48, 51, 63, 75, 83, x and 69 is 60, then the value of x is

Options

A. 52
B. 53
C. 50
D. 51

Answer

To find the value of \( x \) given that the average of the numbers \( 39, 48, 51, 63, 75, 83, x, \) and \( 69 \) is \( 60 \), 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: Identify the number of observations
In this case, we have the numbers \( 39, 48, 51, 63, 75, 83, x, \) and \( 69 \). This gives us a total of \( 8 \) observations.

### Step 3: Set up the equation using the average
We know the average is \( 60 \). Therefore, we can set up the equation:
\[ 60 = \frac{39 + 48 + 51 + 63 + 75 + 83 + x + 69}{8} \]

### Step 4: Calculate the sum of the known numbers
First, we need to calculate the sum of the known numbers:
\[ 39 + 48 + 51 + 63 + 75 + 83 + 69 \]
Calculating this step-by-step:
- \( 39 + 48 = 87 \)
- \( 87 + 51 = 138 \)
- \( 138 + 63 = 201 \)
- \( 201 + 75 = 276 \)
- \( 276 + 83 = 359 \)
- \( 359 + 69 = 428 \)

So, the sum of the known numbers is \( 428 \).

### Step 5: Substitute the sum back into the equation
Now we can substitute the sum back into the average equation:
\[ 60 = \frac{428 + x}{8} \]

### Step 6: Multiply both sides by \( 8 \) to eliminate the fraction
To eliminate the fraction, multiply both sides by \( 8 \):
\[ 60 \times 8 = 428 + x \]
\[ 480 = 428 + x \]

### Step 7: Solve for \( x \)
Now, we can isolate \( x \) by subtracting \( 428 \) from both sides:
\[ x = 480 - 428 \]
\[ x = 52 \]

### Conclusion
Thus, the value of \( x \) is \( 52 \).

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