Understanding the Problem: Finding the Average of Remaining Numbers

We are given the total sum of five numbers and information about the average of the first two and the value of the third number. Our goal is to find the average of the last two numbers.

Key Information Provided

• The sum of five numbers is 655.
• The average of the first two numbers is 80.
• The third number is 101.
• We need to find the average of the remaining two numbers.

Step-by-Step Calculation

Step 1: Calculate the Sum of the First Two Numbers

The average of the first two numbers is given as 80. The formula for the average is:

$ \text{Average} = \frac{\text{Sum of Numbers}}{\text{Count of Numbers}} $

Using this, we can find the sum of the first two numbers:

$ \text{Sum of first two numbers} = \text{Average} \times \text{Count} $

$ \text{Sum of first two numbers} = 80 \times 2 $

$ \text{Sum of first two numbers} = 160 $

Step 2: Calculate the Sum of the First Three Numbers

We know the sum of the first two numbers (160) and the value of the third number (101). To find the sum of the first three numbers, we add these together:

$ \text{Sum of first three numbers} = (\text{Sum of first two numbers}) + (\text{Third number}) $

$ \text{Sum of first three numbers} = 160 + 101 $

$ \text{Sum of first three numbers} = 261 $

Step 3: Calculate the Sum of the Remaining Two Numbers

The total sum of all five numbers is 655. We've calculated the sum of the first three numbers as 261. To find the sum of the remaining two numbers, we subtract the sum of the first three from the total sum:

$ \text{Sum of remaining two numbers} = (\text{Total sum of five numbers}) - (\text{Sum of first three numbers}) $

$ \text{Sum of remaining two numbers} = 655 - 261 $

$ \text{Sum of remaining two numbers} = 394 $

Step 4: Calculate the Average of the Remaining Two Numbers

Now that we have the sum of the remaining two numbers (394), we can find their average. Since there are two numbers, the count is 2:

$ \text{Average of remaining two numbers} = \frac{\text{Sum of remaining two numbers}}{\text{Count of remaining numbers}} $

$ \text{Average of remaining two numbers} = \frac{394}{2} $

$ \text{Average of remaining two numbers} = 197 $

Conclusion

The average of the remaining two numbers is 197.