What three numbers have an average of 834?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 834. This means if we add these three numbers together and divide by 3, we should get 834.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 834 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 834 * 3 = x + y + z
- So, the sum of our three numbers should be: 2502
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2502.
Solution 1:
834, 834, 834
Verification:
(834 + 834 + 834) / 3 = 2502 / 3 ≈ 834
This solution is correct!
Solution 2:
834, 834, 834
Verification:
(834 + 834 + 834) / 3 = 2502 / 3 ≈ 834
This solution is correct!
Solution 3:
1731, 109, 662
Verification:
(1731 + 109 + 662) / 3 = 2502 / 3 ≈ 834
This solution is correct!
Solution 4:
1206, 405, 891
Verification:
(1206 + 405 + 891) / 3 = 2502 / 3 ≈ 834
This solution is correct!
Solution 5:
1680, 286, 536
Verification:
(1680 + 286 + 536) / 3 = 2502 / 3 ≈ 834
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 2502 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.