The average of X, y and z is 6 more than z. The average of x and y is 50. If Y is 6 less than z, then what is the average of Y and z ?

Options

A. 43
B. 38
C. 40
D. 39

Answer

To solve the problem step by step, let's break down the information given in the question:

1. **Understanding the Average of X, Y, and Z**:
- The average of X, Y, and Z is stated to be 6 more than Z.
- Mathematically, this can be expressed as:
\[ \frac{X + Y + Z}{3} = Z + 6 \]
- Multiplying both sides by 3 gives:
\[ X + Y + Z = 3Z + 18 \]
- Rearranging this, we have:
\[ X + Y = 2Z + 18 \quad \text{(Equation 1)} \]

2. **Understanding the Average of X and Y**:
- The average of X and Y is given as 50.
- This can be expressed as:
\[ \frac{X + Y}{2} = 50 \]
- Multiplying both sides by 2 gives:
\[ X + Y = 100 \quad \text{(Equation 2)} \]

3. **Equating the Two Equations**:
- From Equation 1 and Equation 2, we have:
\[ 2Z + 18 = 100 \]
- Solving for Z:
\[ 2Z = 100 - 18 \]
\[ 2Z = 82 \]
\[ Z = 41 \]

4. **Finding Y**:
- We know that Y is 6 less than Z:
\[ Y = Z - 6 \]
- Substituting the value of Z:
\[ Y = 41 - 6 = 35 \]

5. **Calculating the Average of Y and Z**:
- Now we need to find the average of Y and Z:
\[ \text{Average of Y and Z} = \frac{Y + Z}{2} \]
- Substituting the values of Y and Z:
\[ \text{Average} = \frac{35 + 41}{2} = \frac{76}{2} = 38 \]

Thus, the average of Y and Z is **38**.