What three numbers have an average of 642?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 642. This means if we add these three numbers together and divide by 3, we should get 642.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 642 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 642 * 3 = x + y + z
- So, the sum of our three numbers should be: 1926
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1926.
Solution 1:
642, 642, 642
Verification:
(642 + 642 + 642) / 3 = 1926 / 3 ≈ 642
This solution is correct!
Solution 2:
642, 642, 642
Verification:
(642 + 642 + 642) / 3 = 1926 / 3 ≈ 642
This solution is correct!
Solution 3:
1891, 19, 16
Verification:
(1891 + 19 + 16) / 3 = 1926 / 3 ≈ 642
This solution is correct!
Solution 4:
987, 37, 902
Verification:
(987 + 37 + 902) / 3 = 1926 / 3 ≈ 642
This solution is correct!
Solution 5:
1278, 547, 101
Verification:
(1278 + 547 + 101) / 3 = 1926 / 3 ≈ 642
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 1926 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.