What three numbers have an average of 833?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 833. This means if we add these three numbers together and divide by 3, we should get 833.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 833 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 833 * 3 = x + y + z
- So, the sum of our three numbers should be: 2499
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2499.
Solution 1:
833, 833, 833
Verification:
(833 + 833 + 833) / 3 = 2499 / 3 ≈ 833
This solution is correct!
Solution 2:
833, 833, 833
Verification:
(833 + 833 + 833) / 3 = 2499 / 3 ≈ 833
This solution is correct!
Solution 3:
2017, 310, 172
Verification:
(2017 + 310 + 172) / 3 = 2499 / 3 ≈ 833
This solution is correct!
Solution 4:
2371, 28, 100
Verification:
(2371 + 28 + 100) / 3 = 2499 / 3 ≈ 833
This solution is correct!
Solution 5:
868, 473, 1158
Verification:
(868 + 473 + 1158) / 3 = 2499 / 3 ≈ 833
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 2499 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.