What three numbers have an average of 841?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 841. This means if we add these three numbers together and divide by 3, we should get 841.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 841 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 841 * 3 = x + y + z
- So, the sum of our three numbers should be: 2523
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2523.
Solution 1:
841, 841, 841
Verification:
(841 + 841 + 841) / 3 = 2523 / 3 ≈ 841
This solution is correct!
Solution 2:
841, 841, 841
Verification:
(841 + 841 + 841) / 3 = 2523 / 3 ≈ 841
This solution is correct!
Solution 3:
142, 1330, 1051
Verification:
(142 + 1330 + 1051) / 3 = 2523 / 3 ≈ 841
This solution is correct!
Solution 4:
949, 351, 1223
Verification:
(949 + 351 + 1223) / 3 = 2523 / 3 ≈ 841
This solution is correct!
Solution 5:
2106, 107, 310
Verification:
(2106 + 107 + 310) / 3 = 2523 / 3 ≈ 841
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 2523 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.