What three numbers have an average of 859?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 859. This means if we add these three numbers together and divide by 3, we should get 859.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 859 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 859 * 3 = x + y + z
- So, the sum of our three numbers should be: 2577
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2577.
Solution 1:
859, 859, 859
Verification:
(859 + 859 + 859) / 3 = 2577 / 3 ≈ 859
This solution is correct!
Solution 2:
859, 859, 859
Verification:
(859 + 859 + 859) / 3 = 2577 / 3 ≈ 859
This solution is correct!
Solution 3:
1788, 204, 585
Verification:
(1788 + 204 + 585) / 3 = 2577 / 3 ≈ 859
This solution is correct!
Solution 4:
818, 1219, 540
Verification:
(818 + 1219 + 540) / 3 = 2577 / 3 ≈ 859
This solution is correct!
Solution 5:
1716, 212, 649
Verification:
(1716 + 212 + 649) / 3 = 2577 / 3 ≈ 859
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 2577 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.