What three numbers have an average of 856?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 856. This means if we add these three numbers together and divide by 3, we should get 856.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 856 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 856 * 3 = x + y + z
- So, the sum of our three numbers should be: 2568
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2568.
Solution 1:
856, 856, 856
Verification:
(856 + 856 + 856) / 3 = 2568 / 3 ≈ 856
This solution is correct!
Solution 2:
856, 856, 856
Verification:
(856 + 856 + 856) / 3 = 2568 / 3 ≈ 856
This solution is correct!
Solution 3:
811, 356, 1401
Verification:
(811 + 356 + 1401) / 3 = 2568 / 3 ≈ 856
This solution is correct!
Solution 4:
1202, 654, 712
Verification:
(1202 + 654 + 712) / 3 = 2568 / 3 ≈ 856
This solution is correct!
Solution 5:
320, 1695, 553
Verification:
(320 + 1695 + 553) / 3 = 2568 / 3 ≈ 856
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 2568 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.