If the average of x, y and 36 is 24, then find the average of x and y.

Options

A. 10
B. 15
C. 17
D. 18

Answer

To solve the problem step by step, we need to find the average of \( x \) and \( y \) given that the average of \( x \), \( y \), and \( 36 \) is \( 24 \).

### Step 1: Understand the average formula
The average of three numbers \( a, b, c \) is given by the formula:
\[ \text{Average} = \frac{a + b + c}{3} \]
In our case, the numbers are \( x, y, \) and \( 36 \).

### Step 2: Set up the equation
According to the problem, the average of \( x, y, \) and \( 36 \) is \( 24 \). Therefore, we can set up the equation:
\[ \frac{x + y + 36}{3} = 24 \]

### Step 3: Multiply both sides by 3
To eliminate the fraction, we multiply both sides of the equation by \( 3 \):
\[ x + y + 36 = 24 \times 3 \]

### Step 4: Calculate \( 24 \times 3 \)
Calculating the right side gives:
\[ 24 \times 3 = 72 \]
So, we have:
\[ x + y + 36 = 72 \]

### Step 5: Solve for \( x + y \)
Now, we can isolate \( x + y \) by subtracting \( 36 \) from both sides:
\[ x + y = 72 - 36 \]
Calculating the right side gives:
\[ x + y = 36 \]

### Step 6: Find the average of \( x \) and \( y \)
The average of \( x \) and \( y \) is given by:
\[ \text{Average of } x \text{ and } y = \frac{x + y}{2} \]
Substituting \( x + y = 36 \) into this formula:
\[ \text{Average of } x \text{ and } y = \frac{36}{2} \]

### Step 7: Calculate the final answer
Calculating the right side gives:
\[ \text{Average of } x \text{ and } y = 18 \]

Thus, the average of \( x \) and \( y \) is \( 18 \).