What three numbers have an average of 861?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 861. This means if we add these three numbers together and divide by 3, we should get 861.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 861 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 861 * 3 = x + y + z
- So, the sum of our three numbers should be: 2583
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2583.
Solution 1:
861, 861, 861
Verification:
(861 + 861 + 861) / 3 = 2583 / 3 ≈ 861
This solution is correct!
Solution 2:
861, 861, 861
Verification:
(861 + 861 + 861) / 3 = 2583 / 3 ≈ 861
This solution is correct!
Solution 3:
2318, 78, 187
Verification:
(2318 + 78 + 187) / 3 = 2583 / 3 ≈ 861
This solution is correct!
Solution 4:
2258, 146, 179
Verification:
(2258 + 146 + 179) / 3 = 2583 / 3 ≈ 861
This solution is correct!
Solution 5:
536, 608, 1439
Verification:
(536 + 608 + 1439) / 3 = 2583 / 3 ≈ 861
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 2583 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.