What three numbers have an average of 628?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 628. This means if we add these three numbers together and divide by 3, we should get 628.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 628 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 628 * 3 = x + y + z
- So, the sum of our three numbers should be: 1884
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1884.
Solution 1:
628, 628, 628
Verification:
(628 + 628 + 628) / 3 = 1884 / 3 ≈ 628
This solution is correct!
Solution 2:
628, 628, 628
Verification:
(628 + 628 + 628) / 3 = 1884 / 3 ≈ 628
This solution is correct!
Solution 3:
1873, 1, 10
Verification:
(1873 + 1 + 10) / 3 = 1884 / 3 ≈ 628
This solution is correct!
Solution 4:
1063, 688, 133
Verification:
(1063 + 688 + 133) / 3 = 1884 / 3 ≈ 628
This solution is correct!
Solution 5:
267, 328, 1289
Verification:
(267 + 328 + 1289) / 3 = 1884 / 3 ≈ 628
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 1884 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.