What three numbers have an average of 836?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 836. This means if we add these three numbers together and divide by 3, we should get 836.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 836 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 836 * 3 = x + y + z
- So, the sum of our three numbers should be: 2508
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2508.
Solution 1:
836, 836, 836
Verification:
(836 + 836 + 836) / 3 = 2508 / 3 ≈ 836
This solution is correct!
Solution 2:
836, 836, 836
Verification:
(836 + 836 + 836) / 3 = 2508 / 3 ≈ 836
This solution is correct!
Solution 3:
2322, 63, 123
Verification:
(2322 + 63 + 123) / 3 = 2508 / 3 ≈ 836
This solution is correct!
Solution 4:
2482, 20, 6
Verification:
(2482 + 20 + 6) / 3 = 2508 / 3 ≈ 836
This solution is correct!
Solution 5:
2237, 228, 43
Verification:
(2237 + 228 + 43) / 3 = 2508 / 3 ≈ 836
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 2508 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.