What three numbers have an average of 812?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 812. This means if we add these three numbers together and divide by 3, we should get 812.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 812 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 812 * 3 = x + y + z
- So, the sum of our three numbers should be: 2436
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2436.
Solution 1:
812, 812, 812
Verification:
(812 + 812 + 812) / 3 = 2436 / 3 ≈ 812
This solution is correct!
Solution 2:
812, 812, 812
Verification:
(812 + 812 + 812) / 3 = 2436 / 3 ≈ 812
This solution is correct!
Solution 3:
533, 1706, 197
Verification:
(533 + 1706 + 197) / 3 = 2436 / 3 ≈ 812
This solution is correct!
Solution 4:
2174, 48, 214
Verification:
(2174 + 48 + 214) / 3 = 2436 / 3 ≈ 812
This solution is correct!
Solution 5:
1429, 106, 901
Verification:
(1429 + 106 + 901) / 3 = 2436 / 3 ≈ 812
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 2436 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.