What three numbers have an average of 607?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 607. This means if we add these three numbers together and divide by 3, we should get 607.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 607 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 607 * 3 = x + y + z
- So, the sum of our three numbers should be: 1821
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1821.
Solution 1:
607, 607, 607
Verification:
(607 + 607 + 607) / 3 = 1821 / 3 ≈ 607
This solution is correct!
Solution 2:
607, 607, 607
Verification:
(607 + 607 + 607) / 3 = 1821 / 3 ≈ 607
This solution is correct!
Solution 3:
1807, 2, 12
Verification:
(1807 + 2 + 12) / 3 = 1821 / 3 ≈ 607
This solution is correct!
Solution 4:
1296, 438, 87
Verification:
(1296 + 438 + 87) / 3 = 1821 / 3 ≈ 607
This solution is correct!
Solution 5:
1413, 2, 406
Verification:
(1413 + 2 + 406) / 3 = 1821 / 3 ≈ 607
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 1821 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.