Average of 49, 62, 37, 55 and x is 53. What is the value of x ?

Options

A. 68
B. 56
C. 62
D. 76

Answer

To find the value of \( x \) given that the average of the numbers 49, 62, 37, 55, and \( x \) is 53, we can follow these steps:

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

### Step 2: Set up the equation
In this case, we have 5 numbers (49, 62, 37, 55, and \( x \)), and we know the average is 53. Thus, we can set up the equation:
\[ \frac{49 + 62 + 37 + 55 + x}{5} = 53 \]

### Step 3: Calculate the sum of the known numbers
First, we need to calculate the sum of the numbers 49, 62, 37, and 55:
\[ 49 + 62 + 37 + 55 = 203 \]

### Step 4: Substitute the sum back into the equation
Now we can substitute this sum back into our equation:
\[ \frac{203 + x}{5} = 53 \]

### Step 5: Multiply both sides by 5 to eliminate the fraction
To eliminate the fraction, multiply both sides by 5:
\[ 203 + x = 53 \times 5 \]
Calculating \( 53 \times 5 \):
\[ 53 \times 5 = 265 \]
So, we have:
\[ 203 + x = 265 \]

### Step 6: Solve for \( x \)
Now, we can solve for \( x \) by subtracting 203 from both sides:
\[ x = 265 - 203 \]
Calculating the right side:
\[ x = 62 \]

### Final Answer
Thus, the value of \( x \) is \( 62 \).

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