Question

If the mean of 6, 7, x, 8, y, 14 is 9 then x+y=

• A. 17
• B. 18
• C. 19
• D. 20

Answer 1

The Correct Option is C

To solve the problem, we need to determine the value of \( x + y \) given that the mean of the numbers \( 6, 7, x, 8, y, 14 \) is 9.

1. Formula for Mean:
The mean of a set of numbers is the sum of the numbers divided by the total count of the numbers. Here, the mean is given as 9, and the numbers are \( 6, 7, x, 8, y, 14 \). The total count of numbers is 6. Therefore, the formula for the mean is:

\[ \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total count}} \]

Substitute the given values:

\[ 9 = \frac{6 + 7 + x + 8 + y + 14}{6} \]

2. Simplifying the Equation:
First, calculate the sum of the known numbers \( 6, 7, 8, \) and \( 14 \):

\[ 6 + 7 + 8 + 14 = 35 \]

So the equation becomes:

\[ 9 = \frac{35 + x + y}{6} \]

Multiply both sides by 6 to eliminate the denominator:

\[ 9 \times 6 = 35 + x + y \] \[ 54 = 35 + x + y \]

3. Solving for \( x + y \):
Subtract 35 from both sides:

\[ x + y = 54 - 35 \] \[ x + y = 19 \]

4. Final Answer:
The value of \( x + y \) is \( {19} \).