If the average of x, y, and z is 12, what is the average of 3x, 3y, and 3z?

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the average of x, y, and z
We know that the average of three numbers \( x, y, \) and \( z \) is given by the formula:
\[ \text{Average} = \frac{x + y + z}{3} \]
According to the problem, this average is 12.

### Step 2: Set up the equation
From the information given, we can set up the equation:
\[ \frac{x + y + z}{3} = 12 \]

### Step 3: Solve for the sum of x, y, and z
To find the sum \( x + y + z \), we can multiply both sides of the equation by 3:
\[ x + y + z = 12 \times 3 \]
Calculating the right side:
\[ x + y + z = 36 \]

### Step 4: Find the average of 3x, 3y, and 3z
Now, we need to find the average of \( 3x, 3y, \) and \( 3z \). The average is given by:
\[ \text{Average} = \frac{3x + 3y + 3z}{3} \]

### Step 5: Factor out the common term
We can factor out the 3 from the numerator:
\[ \text{Average} = \frac{3(x + y + z)}{3} \]
The 3s in the numerator and denominator cancel out:
\[ \text{Average} = x + y + z \]

### Step 6: Substitute the sum we found
From Step 3, we know that \( x + y + z = 36 \). Therefore:
\[ \text{Average} = 36 \]

### Final Answer
The average of \( 3x, 3y, \) and \( 3z \) is \( 36 \).

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