What three numbers have an average of 835?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 835. This means if we add these three numbers together and divide by 3, we should get 835.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 835 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 835 * 3 = x + y + z
- So, the sum of our three numbers should be: 2505
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2505.
Solution 1:
835, 835, 835
Verification:
(835 + 835 + 835) / 3 = 2505 / 3 ≈ 835
This solution is correct!
Solution 2:
835, 835, 835
Verification:
(835 + 835 + 835) / 3 = 2505 / 3 ≈ 835
This solution is correct!
Solution 3:
2498, 6, 1
Verification:
(2498 + 6 + 1) / 3 = 2505 / 3 ≈ 835
This solution is correct!
Solution 4:
416, 1672, 417
Verification:
(416 + 1672 + 417) / 3 = 2505 / 3 ≈ 835
This solution is correct!
Solution 5:
492, 1767, 246
Verification:
(492 + 1767 + 246) / 3 = 2505 / 3 ≈ 835
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 2505 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.