What three numbers have an average of 633?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 633. This means if we add these three numbers together and divide by 3, we should get 633.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 633 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 633 * 3 = x + y + z
- So, the sum of our three numbers should be: 1899
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1899.
Solution 1:
633, 633, 633
Verification:
(633 + 633 + 633) / 3 = 1899 / 3 ≈ 633
This solution is correct!
Solution 2:
633, 633, 633
Verification:
(633 + 633 + 633) / 3 = 1899 / 3 ≈ 633
This solution is correct!
Solution 3:
439, 750, 710
Verification:
(439 + 750 + 710) / 3 = 1899 / 3 ≈ 633
This solution is correct!
Solution 4:
1488, 262, 149
Verification:
(1488 + 262 + 149) / 3 = 1899 / 3 ≈ 633
This solution is correct!
Solution 5:
703, 342, 854
Verification:
(703 + 342 + 854) / 3 = 1899 / 3 ≈ 633
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 1899 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.