The average (arithmetic mean) of three numbers is 57. If one of the numbers is 16, what is the sum of the other two?

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the concept of average
The average (arithmetic mean) of three numbers is calculated by adding the numbers together and dividing by the total count of numbers.

### Step 2: Write down the formula for the average
The formula for the average of three numbers \( A, B, C \) is:
\[ \text{Average} = \frac{A + B + C}{3} \]
Given that the average is 57, we can set up the equation:
\[ \frac{A + B + C}{3} = 57 \]

### Step 3: Multiply both sides by 3 to eliminate the fraction
To find the sum of the three numbers, multiply both sides of the equation by 3:
\[ A + B + C = 57 \times 3 \]

### Step 4: Calculate the sum
Now, calculate \( 57 \times 3 \):
\[ A + B + C = 171 \]

### Step 5: Substitute the known value
We know one of the numbers is 16. Let's assume \( A = 16 \). Therefore, we can substitute this value into the equation:
\[ 16 + B + C = 171 \]

### Step 6: Solve for the sum of the other two numbers
To find \( B + C \), rearrange the equation:
\[ B + C = 171 - 16 \]

### Step 7: Perform the subtraction
Now, calculate \( 171 - 16 \):
\[ B + C = 155 \]

### Conclusion
The sum of the other two numbers is 155.

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