What three numbers have an average of 842?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 842. This means if we add these three numbers together and divide by 3, we should get 842.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 842 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 842 * 3 = x + y + z
- So, the sum of our three numbers should be: 2526
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2526.
Solution 1:
842, 842, 842
Verification:
(842 + 842 + 842) / 3 = 2526 / 3 ≈ 842
This solution is correct!
Solution 2:
842, 842, 842
Verification:
(842 + 842 + 842) / 3 = 2526 / 3 ≈ 842
This solution is correct!
Solution 3:
1679, 118, 729
Verification:
(1679 + 118 + 729) / 3 = 2526 / 3 ≈ 842
This solution is correct!
Solution 4:
42, 595, 1889
Verification:
(42 + 595 + 1889) / 3 = 2526 / 3 ≈ 842
This solution is correct!
Solution 5:
763, 967, 796
Verification:
(763 + 967 + 796) / 3 = 2526 / 3 ≈ 842
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 2526 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.