What three numbers have an average of 813?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 813. This means if we add these three numbers together and divide by 3, we should get 813.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 813 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 813 * 3 = x + y + z
- So, the sum of our three numbers should be: 2439
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2439.
Solution 1:
813, 813, 813
Verification:
(813 + 813 + 813) / 3 = 2439 / 3 ≈ 813
This solution is correct!
Solution 2:
813, 813, 813
Verification:
(813 + 813 + 813) / 3 = 2439 / 3 ≈ 813
This solution is correct!
Solution 3:
818, 727, 894
Verification:
(818 + 727 + 894) / 3 = 2439 / 3 ≈ 813
This solution is correct!
Solution 4:
1312, 996, 131
Verification:
(1312 + 996 + 131) / 3 = 2439 / 3 ≈ 813
This solution is correct!
Solution 5:
314, 965, 1160
Verification:
(314 + 965 + 1160) / 3 = 2439 / 3 ≈ 813
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 2439 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.