What three numbers have an average of 634?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 634. This means if we add these three numbers together and divide by 3, we should get 634.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 634 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 634 * 3 = x + y + z
- So, the sum of our three numbers should be: 1902
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1902.
Solution 1:
634, 634, 634
Verification:
(634 + 634 + 634) / 3 = 1902 / 3 ≈ 634
This solution is correct!
Solution 2:
634, 634, 634
Verification:
(634 + 634 + 634) / 3 = 1902 / 3 ≈ 634
This solution is correct!
Solution 3:
1854, 28, 20
Verification:
(1854 + 28 + 20) / 3 = 1902 / 3 ≈ 634
This solution is correct!
Solution 4:
119, 1301, 482
Verification:
(119 + 1301 + 482) / 3 = 1902 / 3 ≈ 634
This solution is correct!
Solution 5:
1635, 180, 87
Verification:
(1635 + 180 + 87) / 3 = 1902 / 3 ≈ 634
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 1902 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.