If the mean of 2, x, and y is 8, then the mean of x,y and 8 is________

Options

A. 8
B. 9
C. 12
D. 10

Answer

To solve the problem step by step, we need to find the mean of the numbers \( x \), \( y \), and \( 8 \) given that the mean of \( 2 \), \( x \), and \( y \) is \( 8 \).

### Step 1: Understand the Mean
The mean of a set of numbers is calculated by dividing the sum of the numbers by the count of the numbers.

### Step 2: Set Up the Equation for the Given Mean
We know that the mean of \( 2 \), \( x \), and \( y \) is \( 8 \). We can express this mathematically as:
\[ \text{Mean} = \frac{2 + x + y}{3} = 8 \]

### Step 3: Solve for the Sum of \( 2 \), \( x \), and \( y \)
To find the sum of \( 2 \), \( x \), and \( y \), we can multiply both sides of the equation by \( 3 \):
\[ 2 + x + y = 8 \times 3 \]
\[ 2 + x + y = 24 \]

### Step 4: Rearrange to Find \( x + y \)
Now, we can isolate \( x + y \) by subtracting \( 2 \) from both sides:
\[ x + y = 24 - 2 \]
\[ x + y = 22 \]

### Step 5: Find the Mean of \( x \), \( y \), and \( 8 \)
Next, we need to find the mean of \( x \), \( y \), and \( 8 \). The mean can be calculated as follows:
\[ \text{Mean} = \frac{x + y + 8}{3} \]

### Step 6: Substitute \( x + y \) into the Mean Formula
We already found that \( x + y = 22 \). Now, substitute this value into the mean formula:
\[ \text{Mean} = \frac{22 + 8}{3} \]
\[ \text{Mean} = \frac{30}{3} \]

### Step 7: Calculate the Final Mean
Now, divide \( 30 \) by \( 3 \):
\[ \text{Mean} = 10 \]

### Final Answer
The mean of \( x \), \( y \), and \( 8 \) is \( 10 \).

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