What three numbers have an average of 824?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 824. This means if we add these three numbers together and divide by 3, we should get 824.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 824 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 824 * 3 = x + y + z
- So, the sum of our three numbers should be: 2472
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2472.
Solution 1:
824, 824, 824
Verification:
(824 + 824 + 824) / 3 = 2472 / 3 ≈ 824
This solution is correct!
Solution 2:
824, 824, 824
Verification:
(824 + 824 + 824) / 3 = 2472 / 3 ≈ 824
This solution is correct!
Solution 3:
1787, 538, 147
Verification:
(1787 + 538 + 147) / 3 = 2472 / 3 ≈ 824
This solution is correct!
Solution 4:
1013, 570, 889
Verification:
(1013 + 570 + 889) / 3 = 2472 / 3 ≈ 824
This solution is correct!
Solution 5:
2125, 305, 42
Verification:
(2125 + 305 + 42) / 3 = 2472 / 3 ≈ 824
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 2472 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.