What three numbers have an average of 658?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 658. This means if we add these three numbers together and divide by 3, we should get 658.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 658 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 658 * 3 = x + y + z
- So, the sum of our three numbers should be: 1974
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1974.
Solution 1:
658, 658, 658
Verification:
(658 + 658 + 658) / 3 = 1974 / 3 ≈ 658
This solution is correct!
Solution 2:
658, 658, 658
Verification:
(658 + 658 + 658) / 3 = 1974 / 3 ≈ 658
This solution is correct!
Solution 3:
1049, 819, 106
Verification:
(1049 + 819 + 106) / 3 = 1974 / 3 ≈ 658
This solution is correct!
Solution 4:
199, 1332, 443
Verification:
(199 + 1332 + 443) / 3 = 1974 / 3 ≈ 658
This solution is correct!
Solution 5:
1142, 748, 84
Verification:
(1142 + 748 + 84) / 3 = 1974 / 3 ≈ 658
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 1974 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.