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:
1268, 564, 142
Verification:
(1268 + 564 + 142) / 3 = 1974 / 3 ≈ 658
This solution is correct!
Solution 4:
1388, 227, 359
Verification:
(1388 + 227 + 359) / 3 = 1974 / 3 ≈ 658
This solution is correct!
Solution 5:
118, 484, 1372
Verification:
(118 + 484 + 1372) / 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.