What three numbers have an average of 826?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 826. This means if we add these three numbers together and divide by 3, we should get 826.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 826 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 826 * 3 = x + y + z
- So, the sum of our three numbers should be: 2478
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2478.
Solution 1:
826, 826, 826
Verification:
(826 + 826 + 826) / 3 = 2478 / 3 ≈ 826
This solution is correct!
Solution 2:
826, 826, 826
Verification:
(826 + 826 + 826) / 3 = 2478 / 3 ≈ 826
This solution is correct!
Solution 3:
1104, 257, 1117
Verification:
(1104 + 257 + 1117) / 3 = 2478 / 3 ≈ 826
This solution is correct!
Solution 4:
841, 1337, 300
Verification:
(841 + 1337 + 300) / 3 = 2478 / 3 ≈ 826
This solution is correct!
Solution 5:
1977, 268, 233
Verification:
(1977 + 268 + 233) / 3 = 2478 / 3 ≈ 826
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 2478 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.