The average of three numbers is 20. If two of the numbers are 16 and 22, the third is-

Options

A. 18
B. 19
C. 20
D. 22

Answer

To find the third number when the average of three numbers is given, we can follow these steps:

### Step 1: Understand the formula for average
The average of a set of numbers is calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of the numbers}}{\text{Total number of values}} \]

### Step 2: Set up the equation
Given that the average of three numbers is 20, we can express this as:
\[ 20 = \frac{16 + 22 + x}{3} \]
where \( x \) is the third number we need to find.

### Step 3: Multiply both sides by 3
To eliminate the fraction, we multiply both sides of the equation by 3:
\[ 60 = 16 + 22 + x \]

### Step 4: Simplify the right side
Now, we can simplify the right side:
\[ 60 = 38 + x \]

### Step 5: Solve for \( x \)
To find \( x \), we subtract 38 from both sides:
\[ x = 60 - 38 \]
\[ x = 22 \]

### Conclusion
The third number is \( 22 \).

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