The average of 9, 11, and 16 is equal to the average of 21, 4.6, and what number ?

Answer

To solve the problem step by step, we need to find the unknown number \( x \) such that the average of the numbers 9, 11, and 16 is equal to the average of the numbers 21, 4.6, and \( x \).

### Step 1: Calculate the average of 9, 11, and 16

The average is calculated using the formula:

\[ \text{Average} = \frac{\text{Sum of values}}{\text{Number of values}} \]

For the numbers 9, 11, and 16:

\[ \text{Sum} = 9 + 11 + 16 = 36 \]

The number of values is 3. Therefore, the average is:

\[ \text{Average} = \frac{36}{3} = 12 \]

### Step 2: Set up the equation for the average of 21, 4.6, and \( x \)

The average of the numbers 21, 4.6, and \( x \) can be expressed as:

\[ \text{Average} = \frac{21 + 4.6 + x}{3} \]

### Step 3: Set the two averages equal to each other

Since the average of 9, 11, and 16 is equal to the average of 21, 4.6, and \( x \), we can set up the equation:

\[ 12 = \frac{21 + 4.6 + x}{3} \]

### Step 4: Multiply both sides by 3 to eliminate the denominator

To eliminate the fraction, multiply both sides by 3:

\[ 12 \times 3 = 21 + 4.6 + x \]

This simplifies to:

\[ 36 = 21 + 4.6 + x \]

### Step 5: Simplify the right side of the equation

Now, calculate \( 21 + 4.6 \):

\[ 21 + 4.6 = 25.6 \]

So the equation now is:

\[ 36 = 25.6 + x \]

### Step 6: Solve for \( x \)

To find \( x \), subtract 25.6 from both sides:

\[ x = 36 - 25.6 \]

Calculating this gives:

\[ x = 10.4 \]

### Final Answer

The unknown number \( x \) is:

\[ \boxed{10.4} \]