What three numbers have an average of 820?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 820. This means if we add these three numbers together and divide by 3, we should get 820.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 820 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 820 * 3 = x + y + z
- So, the sum of our three numbers should be: 2460
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2460.
Solution 1:
820, 820, 820
Verification:
(820 + 820 + 820) / 3 = 2460 / 3 ≈ 820
This solution is correct!
Solution 2:
820, 820, 820
Verification:
(820 + 820 + 820) / 3 = 2460 / 3 ≈ 820
This solution is correct!
Solution 3:
684, 1463, 313
Verification:
(684 + 1463 + 313) / 3 = 2460 / 3 ≈ 820
This solution is correct!
Solution 4:
1109, 103, 1248
Verification:
(1109 + 103 + 1248) / 3 = 2460 / 3 ≈ 820
This solution is correct!
Solution 5:
1137, 346, 977
Verification:
(1137 + 346 + 977) / 3 = 2460 / 3 ≈ 820
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 2460 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.