What three numbers have an average of 822?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 822. This means if we add these three numbers together and divide by 3, we should get 822.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 822 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 822 * 3 = x + y + z
- So, the sum of our three numbers should be: 2466
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2466.
Solution 1:
822, 822, 822
Verification:
(822 + 822 + 822) / 3 = 2466 / 3 ≈ 822
This solution is correct!
Solution 2:
822, 822, 822
Verification:
(822 + 822 + 822) / 3 = 2466 / 3 ≈ 822
This solution is correct!
Solution 3:
949, 1467, 50
Verification:
(949 + 1467 + 50) / 3 = 2466 / 3 ≈ 822
This solution is correct!
Solution 4:
171, 2089, 206
Verification:
(171 + 2089 + 206) / 3 = 2466 / 3 ≈ 822
This solution is correct!
Solution 5:
126, 1906, 434
Verification:
(126 + 1906 + 434) / 3 = 2466 / 3 ≈ 822
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 2466 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.