What three numbers have an average of 657?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 657. This means if we add these three numbers together and divide by 3, we should get 657.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 657 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 657 * 3 = x + y + z
- So, the sum of our three numbers should be: 1971
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1971.
Solution 1:
657, 657, 657
Verification:
(657 + 657 + 657) / 3 = 1971 / 3 ≈ 657
This solution is correct!
Solution 2:
657, 657, 657
Verification:
(657 + 657 + 657) / 3 = 1971 / 3 ≈ 657
This solution is correct!
Solution 3:
648, 681, 642
Verification:
(648 + 681 + 642) / 3 = 1971 / 3 ≈ 657
This solution is correct!
Solution 4:
693, 377, 901
Verification:
(693 + 377 + 901) / 3 = 1971 / 3 ≈ 657
This solution is correct!
Solution 5:
1748, 82, 141
Verification:
(1748 + 82 + 141) / 3 = 1971 / 3 ≈ 657
This solution is correct!
Explanation:
As you can see, there are many possible solutions. We can find more by:
- Choosing any two numbers
- Subtracting their sum from 1971 to get the third number
Remember:
- The numbers don't have to be whole numbers.
- They can even be negative (although that might not make sense in some real-world contexts).
- The order of the numbers doesn't matter for the average.